In a large mixing bowl, combine warm milk, a pinch of sugar, and active dry yeast. Stir gently, then let it stand in a warm spot for 5 to 10 minutes until foamy.

Whisk in the remaining sugar, egg, vanilla extract, salt, and melted butter until smooth.

Gradually add all-purpose flour to the wet mixture, stirring until a soft dough forms. Transfer to a floured surface and knead for 5 to 7 minutes until smooth and elastic.

Place the kneaded dough in a greased bowl and cover with a towel. Allow it to rise in a warm area for 1 to 1.5 hours, or until it doubles in size.

Punch down the dough gently and roll it out to about 1/4 inch thickness. Cut the dough into 2–3 inch squares or rectangles.

Heat vegetable oil to 350°F (175°C) in a deep fryer or large pot. Fry the beignet pieces a few at a time for 1 to 2 minutes on each side until golden brown and puffed.

Remove the beignets from the oil and drain them on paper towels. Dust generously with powdered sugar and serve immediately.