Step 1: Activate the Yeast : In a small bowl, combine warm milk and sugar. Sprinkle yeast over the top and let it sit for 5–10 minutes until frothy and activated.

Step 2: Make the Dough : In a large mixing bowl, whisk together flour and salt. Add eggs, softened butter, vanilla, and the yeast mixture. Mix until a soft dough forms. Knead the dough on a floured surface for about 5–7 minutes until smooth and elastic.

Step 3: Let the Dough Rise : Place the dough in a greased bowl, cover it with a kitchen towel or plastic wrap, and let it rise for 1 hour in a warm spot — or until doubled in size.

Step 4: Shape the Donuts : Once risen, punch down the dough and roll it out on a floured surface to about ½-inch thickness.

Cut out donuts using a 3-inch donut cutter (or use a large cup and a smaller one for the hole). Place the shaped donuts on parchment paper and let them rest for 15–20 minutes.

Step 5: Fry the Donuts : Heat oil in a deep pan or fryer to 350°F (175°C). Carefully add 2–3 donuts at a time and fry for about 1 minute per side, or until golden brown.

Remove with a slotted spoon and drain on paper towels.

Step 6: Make the Chocolate Glaze : In a medium bowl, whisk together powdered sugar, cocoa powder, milk, vanilla, and melted butter until smooth and glossy. Adjust with a little more milk if needed for a thinner glaze.

Step 7: Glaze the Donuts : Once the donuts have cooled slightly (but are still warm), dip the tops into the chocolate glaze. Place on a wire rack to let the glaze set.