In a small bowl, combine warm water with sugar and yeast. Stir gently, then let it sit for 5-10 minutes until foamy.

In a large mixing bowl, whisk together buttermilk, beaten egg, and melted butter. Gradually add the activated yeast mixture and stir.

Transfer the dough to a greased bowl and cover with a clean towel. Let it rise in a warm place for about 1 hour until doubled in size.

Lightly flour a clean surface and roll out the dough to about ½-inch thickness. Cut into 2-inch squares.

Heat oil to 350°F in a deep pot. Fry the dough squares in batches for 1-2 minutes until golden brown.

Prepare the glaze by whisking powdered sugar, milk, and vanilla extract until smooth. Dip the warm beignets in the glaze.