01 - In a small bowl, dissolve the yeast and 1 teaspoon of sugar in the warm water. Let stand for 5–10 minutes until foamy.
02 - In a large mixing bowl, combine the remaining sugar, milk, egg, melted butter, and salt. Whisk thoroughly until well blended.
03 - Add the yeast mixture to the wet ingredients and mix to combine fully.
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 about 5 minutes until smooth and elastic, or knead in the mixer for 3–4 minutes.
06 - Place 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 dough and transfer to a floured surface. Roll out to about 1/4 inch thickness. Using a sharp knife or pizza cutter, cut the dough into 2-inch squares.
08 - Heat the 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. While still warm, generously dust with powdered sugar and serve immediately.