Prepare the Dough:

1. Activate the Yeast: In a small bowl, mix the warm milk with the yeast and sugar. Stir until the yeast dissolves, then let it sit for 5-10 minutes until it becomes frothy. This step ensures the yeast is activated and will give the doughnuts their signature fluffiness.
2. Combine Wet Ingredients: In a large mixing bowl, beat the eggs and softened butter together until smooth. Stir in the vanilla extract.
3. Add Yeast Mixture to Wet Ingredients: Once the yeast mixture is frothy, pour it into the egg and butter mixture. Stir to combine.
4. Add Dry Ingredients: In a separate bowl, mix the flour, salt, and optional cinnamon. Gradually add the dry ingredients to the wet ingredients, stirring until a dough starts to form. It will be slightly sticky but should come together.
5. Knead the Dough: Transfer the dough to a lightly floured surface. Knead the dough for about 8-10 minutes, or until it becomes smooth and elastic. If the dough is too sticky, sprinkle a little more flour on it, but try to keep the dough soft and moist.

Let the Dough Rise:

6. First Rise: Place the kneaded dough in a greased bowl. Cover the bowl with a clean kitchen towel or plastic wrap. Let the dough rise in a warm place for about 1 to 1.5 hours, or until it has doubled in size.

Shape the Doughnuts:

7. Roll the Dough: Once the dough has risen, gently punch it down to release the air. Turn the dough out onto a floured surface and roll it to about ½-inch thickness.
8. Cut the Doughnuts: Use a round cutter to cut out doughnut shapes. For the center hole, use a smaller round cutter, or you can use a bottle cap if you don’t have a specialized cutter. Gather any leftover dough and re-roll it to make more doughnuts.

Fry the Doughnuts:

9. Heat the Oil: In a large pot or deep fryer, heat vegetable oil to 350°F (175°C). To test if the oil is ready, drop in a small piece of dough—if it floats to the surface and begins to brown quickly, the oil is hot enough.
10. Fry the Doughnuts: Carefully place a few doughnuts into the hot oil, being careful not to overcrowd the pot. Fry them for 2-4 minutes on each side, or until golden brown. Use a slotted spoon to remove the doughnuts from the oil and transfer them to a paper towel-lined plate to drain excess oil.

Glaze or Coat the Doughnuts:

11. Coat with Sugar or Glaze: Once the doughnuts have cooled slightly, you can dip them in your favorite toppings:
    • Powdered Sugar Coating: Dust the doughnuts with powdered sugar for a simple, classic touch.
    • Cinnamon-Sugar: Mix granulated sugar and cinnamon in a shallow bowl and roll the doughnuts in the mixture.
    • Glazed Doughnuts: For a glossy finish, dip the warm doughnuts in a simple glaze made from powdered sugar, milk, and vanilla extract. Adjust the consistency by adding more milk if needed.

Serve:

12. Enjoy: Once your doughnuts are glazed or coated to your liking, serve them immediately with a hot cup of tea or coffee. These doughnuts are best enjoyed fresh, but you can store them in an airtight container for a couple of days.