In a large bowl, combine warm milk, yeast, and a pinch of sugar. Let it stand for about 5-10 minutes until it becomes foamy.

Whisk in the remaining granulated sugar, egg, vanilla extract, salt, and melted butter into the yeast mixture.

Gradually add the flour, mixing until a soft dough forms. Knead this dough on a lightly floured surface for about 5-7 minutes until it becomes smooth and elastic.

Place the dough in a greased bowl, cover it, and let it rise in a warm place for 1 to 1.5 hours or until the dough has doubled in size.

Once the dough has risen, punch it down to remove excess air. Roll it out to about 1/4 inch thickness and cut into 2-3 inch squares or rectangles.

Heat vegetable oil in a deep fryer or large pot to 350 degrees F (175 degrees C). Fry the beignets a few at a time for about 1-2 minutes per side until they are golden brown and puffed up.

Remove the beignets with a slotted spoon and drain them on paper towels. Dust generously with powdered sugar before serving warm.