01 - Dissolve yeast and 1 teaspoon sugar in warm water. Let stand until foamy, about 5 minutes.
02 - In a large mixing bowl, whisk together flour, remaining sugar, and salt.
03 - In a separate bowl, whisk milk, eggs, melted butter, and vanilla until combined.
04 - Pour yeast mixture and milk mixture into dry ingredients. Stir until a sticky dough forms.
05 - Turn dough onto a lightly floured surface and knead 5 to 7 minutes until smooth and elastic.
06 - Place dough in a greased bowl, cover, and let rise in a warm spot until doubled, about 1 to 1.5 hours.
07 - Punch down dough, roll to 1/4-inch thickness, and cut into 2-inch squares.
08 - Heat vegetable oil to 350°F in a deep fryer or heavy pot.
09 - Fry beignets in batches, flipping once, until puffed and golden brown, 1 to 2 minutes per side.
10 - Remove with a slotted spoon and drain on paper towels.
11 - Generously dust warm beignets with powdered sugar and serve immediately.