Creating these glazed donuts is a simple yet rewarding process. Follow these steps to achieve donut perfection:

Step 1: Prepare the Dough

1. Activate the Yeast: In a small bowl, combine the warmed milk and yeast. Stir gently and let it sit for about 5 minutes, or until it becomes frothy.
2. Mix the Dry Ingredients: In a large mixing bowl, whisk together the flour, sugar, and salt.
3. Combine Wet Ingredients: In another bowl, mix the eggs, vanilla extract, and melted butter.
4. Form the Dough: Create a well in the center of the dry ingredients. Pour in the yeast mixture and the wet ingredients. Stir until a dough forms.
5. Knead the Dough: Transfer the dough to a floured surface and knead for about 8-10 minutes, until it becomes smooth and elastic.

Step 2: Let the Dough Rise

6. First Rise: Place the kneaded dough in a greased bowl, cover it with a damp cloth, and let it rise in a warm area for about 1-2 hours, or until doubled in size.

Step 3: Shape the Donuts

7. Roll Out the Dough: Once the dough has risen, punch it down to release air. Roll it out on a floured surface to about ½ inch thickness.
8. Cut the Donuts: Use a donut cutter or two round cutters (one larger and one smaller for the center hole) to cut out the donuts. Re-roll the scraps to make more donuts.
9. Second Rise: Place the cut donuts on a baking sheet lined with parchment paper. Cover with a towel and let them rise for another 30 minutes.

Step 4: Fry the Donuts

10. Heat the Oil: In a large, deep pot, heat oil to 350°F. Ensure there’s enough oil to allow the donuts to float freely.
11. Fry the Donuts: Carefully place a few donuts at a time into the hot oil. Fry each side for about 1-2 minutes, or until golden brown. Remove with a slotted spoon and drain on paper towels.

Step 5: Glaze the Donuts

12. Prepare the Glaze: In a bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth.
13. Dip the Donuts: While the donuts are still warm, dip the top of each donut into the glaze. Allow the excess to drip off before placing them back on the rack.