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