In a small bowl, combine warm water, sugar, and active dry yeast. Stir and let sit for 5–10 minutes until frothy.

In a large bowl, whisk together buttermilk, egg, and melted butter. Add the yeast mixture, then gradually add flour and salt, stirring until a sticky dough forms.

Knead the dough on a floured surface for 5–7 minutes until smooth. Shape into a ball, place in a greased bowl, cover, and let rise for 1–2 hours until doubled.

Punch down the dough, roll to 1/2 inch thickness, and cut into 2-inch squares for frying.

Heat oil to 350°F. Fry beignet squares in small batches for 1–2 minutes until golden brown. Drain on a wire rack.

Whisk together powdered sugar, milk, and vanilla in a medium bowl to create a glaze. Adjust consistency as needed.

Dip warm beignets in glaze, ensure well coated, and let set on a wire rack before serving.