1. In a large bowl, mix together 2 cups of all-purpose flour and 4 tablespoons of sugar.
2. In a separate bowl, whisk one packet of active dry yeast and 1/4 cup of warm water until the mixture is frothy.
3. Pour the yeast mixture into the flour and sugar mixture, then mix until fully combined.
4. Add in 1/4 cup of melted butter, 1 teaspoon of vanilla extract, 1/4 teaspoon of salt, 1/4 cup of warm milk, and 1 egg.
5. Knead the dough until it is smooth and elastic.
6. Place the dough into a greased bowl, cover with a damp towel, and allow the dough to double in size.
7. Roll the dough out onto a lightly floured surface and use a doughnut cutter to cut out the shapes.
8. Heat at least 2 inches of vegetable oil in a deep-fry pan on medium heat.
9. Carefully place the doughnut shapes into the hot oil and allow them to cook for about 2 minutes on each side.
10. Use a slotted spoon to remove the cooked doughnuts onto a plate lined with paper towels.
11. Dust the doughnuts with sugar and serve.
