• Line two large baking pans with parchment paper.
• Place a cooling rack over a third baking pan.
• Prepare fresh raspberry glaze through Step 1 (see below) and set aside.

for the yeast doughnuts:

• Pour warmed milk (I warm the milk in 5 to 10-second intervals in microwave, testing temperature after each heating) into bowl of stand mixer and then sprinkle yeast evenly over the top of the milk. Let it sit for 1 minute and then give it a small, gentle stir. Let mixture sit for about 5 more minutes, until silky/foamy.
• Preheat oven to 200° F.
• Fit stand mixer with dough hook and then beat sugar, eggs, butter, vanilla, and salt into yeast mixture on low speed, just until combined. Add 2 cups of the flour and mix, just until combined. Then add the remaining 2-1/4 cups of flour, beating on low speed until combined, and then on medium-high speed until the dough pulls away from the sides of bowl. This takes almost 5 minutes of beating time with my mixer. The dough should be thick, yet soft and somewhat sticky. If your dough is too wet, add 1 to 2 tablespoons of flour more. But really try to not add too much more flour, as this will take away from the tenderness of the dough.
• Transfer dough to a lightly floured surface and gently knead until smooth and elastic, about 2 minutes. Pull in a little extra flour as needed. I find it very helpful, almost essential, to use a flexible dough scraper to scrape all the dough out of the bowl (with the curved edge) and to aid in scraping the dough from the kneading surface (with the flat edge) - I almost use the scraper like my second hand. I HIGHLY recommend that you have one of these before starting this recipe. I have grown to love this tool when working with any yeast doughs. Lightly spray a large bowl with non-stick cooking spray and transfer dough to the bowl, turning the dough to coat evenly. Cover bowl with plastic wrap. Turn oven heat off and place bowl of dough in lightly warmed oven. Let dough rise until it doubles in size, about 1 hour. To test if the dough is ready, poke one finger about 1" deep into the top of the dough. If the indent stays, the dough is ready. If the indent fills in with surrounding dough, the dough needs more time to rise.
• Again, preheat oven to 200° F.
• Remove bowl from oven and punch down dough to release air bubbles. Remove dough from bowl and turn it out onto a lightly floured surface. Punch down again, if needed. Then roll dough out to a 1/2" thickness with a lightly floured rolling pin. Use a donut cutter or two circle cookie cutters (large cutter should be about 3-1/2" in diameter) to cut out donuts, dipping the cutters in flour after each cut. You will need to re-roll dough scraps to cut a total of 12 donuts.
• Transfer cut dough to prepared parchment-lined baking pans with a thin metal spatula, 6 donuts and their holes per baking sheet. I found that it worked best for me to transfer the donut and its hole, intact, from the rolled dough surface to the prepared pan, and then remove the hole from the center. Reserve the holes, adding them to the pans with the donuts. Cover each pan gently with a lightweight kitchen towel. Turn oven heat off, place towel-covered dough in oven, and leave oven door ajar. Let dough rest in warmed oven for 30 minutes.
• While dough is resting in the warmed oven, prepare oil for frying. I use an electric deep fryer, but any heavy-bottomed pot or Dutch oven will work. Either way, be sure to use a reliable cooking thermometer to measure the heat of the oil. I found that the attached thermometer on our deep fryer was no longer very accurate (we received the fryer when we were married over 17 years ago), so I learned to rely on my cooking thermometer instead. Add a neutral oil to fryer or pot, to a depth of almost 3".
• Heat to 375°F. This will take quite awhile, and the oil will be very hot. Be careful.
• Also while dough is resting and oil is heating, finish making the fresh raspberry glaze, continuing on with Step 2 (see below). Set glaze aside.
• When oil is heated, add two to three donuts at a time and cook for 1 minute per side. Carefully remove with a metal spatula or metal slotted spoon and place on prepared rack sitting on a baking sheet. The method I like best is to cook two donuts at a time, and when the second set of two donuts is removed from the fryer, I dip the first set of two donuts into the glaze. To achieve a smooth looking glaze, it works best to dip the donuts while they are still very warm. If you want to mix things up, roll the doughnuts in cinnamon sugar - my family loves this! This was also an easy way to finish off the donut holes - by simply placing all the holes in a small bowl, shaking cinnamon sugar over them, and rolling the bowl to evenly coat all the holes.

for the fresh raspberry glaze:

• In a small to medium-sized saucepan over medium heat, stir together raspberries, lemon juice, water, and sugar. When mixture starts to bubble, smash raspberries with the back side of a wooden spoon. Turn heat down a bit to medium-low and let mixture cook for 2 minutes, stirring once or twice.
• Remove pan from heat and stir in vanilla. Line a colander with a double layer of cheese cloth and place over a large bowl. Pour raspberry mixture over cheese cloth. Pull up sides of cheese cloth to form a bundle of raspberry mixture. Then gently press on the bundle with the back side of a large wooden spoon to extract the juices, letting the juices drain into the bowl below. Take care to not pierce and break the cheese cloth. Keep pressing until you have a little more than 1/4 cup of bright red raspberry juice. Set juice aside. Discard the cheese cloth bundle.
• To create the glaze, in a small bowl that's wide enough to dip a donut in, whisk together 1/4 cup of prepared raspberry juice with 1/2 cup of powdered sugar until smooth. Whisk in another 1/2 cup of powdered sugar, and then another, to equal 1-1/2 cups total. Add up to 1/2 cup more of powdered sugar to reach your desired consistency. I found that I liked the glaze somewhere between fluid and thickened. I know that's not much of a measure, but if when you dip your first donut you don't like the consistency, simply add a bit more juice to thin, or a bit more powdered sugar to thicken. I also think it helps to whisk the glaze before dipping if the glaze has been sitting for awhile.