Activate the yeast by combining warm water with a teaspoon of sugar and sprinkling the active dry yeast. Let it sit for 5-10 minutes until frothy.

In a mixing bowl, whisk buttermilk, egg, and melted butter until combined. Fold in the yeast mixture, then stir in flour and salt until a soft dough forms.

Knead the dough on a floured surface for 5-7 minutes until smooth and elastic. Let it rise in a greased bowl covered with a damp cloth for 1 to 2 hours.

Roll the risen dough into 1/2-inch thickness and cut into 2-inch squares.

Heat oil to 350°F. Fry beignet squares in small batches for 1-2 minutes per side until golden brown.

Whisk together powdered sugar, milk, and vanilla extract to make the glaze. Adjust milk for desired consistency.

Dip warm beignets in glaze and let excess drip off before placing them on a wire rack.