01 - Dissolve the yeast and 1 teaspoon of sugar in the warm water. Let stand for 5–10 minutes until foamy and activated.
02 - In a large mixing bowl, whisk together the remaining sugar, milk, egg, melted butter, and salt until well combined.
03 - Pour the activated yeast mixture into the bowl with the wet ingredients and mix thoroughly to incorporate.
04 - Gradually add the flour, stirring with a wooden spoon or using a stand mixer with a dough hook, until a sticky dough forms.
05 - Transfer the dough to a lightly floured surface and knead for approximately 5 minutes until smooth and elastic, or 3–4 minutes in a stand mixer.
06 - Place the dough in a lightly oiled bowl, cover with plastic wrap or a damp towel, and let rise in a warm place until doubled in size, about 1–1.5 hours.
07 - Punch down the risen dough and transfer to a floured surface. Roll out to 1/4 inch thickness and cut into 2-inch squares using a sharp knife or pizza cutter.
08 - Heat vegetable oil in a deep fryer or large heavy-bottomed pot to 350°F.
09 - Fry the dough squares in batches, turning once, until puffed and golden brown on both sides, about 1–2 minutes per side.
10 - Remove beignets with a slotted spoon and drain on paper towels. Generously dust with powdered sugar while still warm and serve immediately.