In a small bowl, combine ¼ cup of warm water and 1 tablespoon of sugar, then sprinkle 2¼ teaspoons of active dry yeast. Let sit for 5–10 minutes until frothy.

In a large mixing bowl, whisk together 1 cup of buttermilk, 1 large egg, and 3 tablespoons of melted butter until smooth. Fold in the frothy yeast mixture, then gradually add 3 cups of all-purpose flour and 1 teaspoon of salt, stirring until a sticky dough forms.

Transfer the dough onto a floured surface and knead for about 5–7 minutes until smooth and elastic. Place in a greased bowl and cover with a kitchen towel. Let it rise in a warm area for 1–2 hours or until doubled in size.

Once risen, punch dough down. Roll out to about ½ inch thick and cut into 2-inch squares using a sharp knife or pizza cutter.

Heat 2–3 inches of neutral oil to 350°F in a deep pot. Fry beignet squares for 1–2 minutes on each side until golden brown. Use a slotted spoon to remove and let drain on a wire rack.

Prepare the glaze by whisking together 2 cups of powdered sugar, ¼ cup of milk, and 1 teaspoon of vanilla extract until smooth. Adjust consistency with more milk if needed.

Once slightly cooled, dip each beignet into the glaze to fully coat. Place on a rack to allow the glaze to set and serve warm.