Step 1

In the bowl of a stand mixer, combine the warm water and yeast. Let sit for 5 minutes until foamy.

Step 2

Warm the milk in a microwave-safe bowl (about 2 minutes), and let it cool to lukewarm.

Step 3

Add the milk, sugar, salt, eggs, butter, and 2 cups of flour to the yeast mixture. Using the paddle attachment, mix at medium speed until smooth and combined.

Step 4

Gradually add the remaining 3 cups of flour and switch to the dough hook attachment. Knead at medium speed for about 5 to 7 minutes or until the dough is soft, smooth, and slightly sticky.

Step 5

Transfer the dough to a large, greased bowl, turning once to coat. Cover it loosely with a clean kitchen towel. Let it rise in a warm, draft-free spot for 1-2 hours or until doubled in size.

Step 6

Once risen, turn the dough out onto a lightly floured surface. Roll to 1/4-inch thickness. Use a doughnut cutter or two round cutters (3-4 inches for the outer circle, 1 inch for the center) to cut out doughnuts. Re-roll scraps as needed.

Step 7

Place the cut doughnuts and holes onto a parchment-lined baking sheet. (Leave a bit of space between them.) Cover loosely and let rest for 10-15 minutes while heating the oil.

Step 8

Heat 3 inches of oil in a large, deep saucepan to 375 degrees Fahrenheit. (Use a thermometer for accuracy.)

Step 9

Working in batches, carefully fry the doughnuts. Fry for about 1-2 minutes per side, turning once, until golden brown. Remove with a slotted spoon and drain on a paper towel-lined tray.

Step 10

In a medium bowl, whisk together confectioners’ sugar, vanilla, and 3 tablespoons of milk until smooth. Add more milk, one tablespoon at a time, until the glaze is thin enough to dip but not too runny.

Step 11

Dip each warm doughnut (top side down) into the glaze. Let the excess drip off. Place on a wire rack to set for a few minutes. Serve, and enjoy!