In a large bowl, combine the flour, granulated sugar, yeast, and salt. Mix well.

In a separate bowl, whisk together the warm milk, melted butter, and vanilla extract.

Gradually pour the wet ingredients into the dry ingredients while stirring until a dough begins to form.

Transfer the dough onto a lightly floured surface and knead for about 8-10 minutes until smooth and elastic.

Place the kneaded dough into a greased bowl, cover, and let it rise in a warm place for about 1.5 hours or until doubled in size.

Punch down the dough, roll it out to about 1/4 inch thickness, and cut into 2x2 inch squares.

Heat about 2 inches of vegetable oil in a deep fryer or large pot to 360°F.

Fry the beignets in batches for about 1-2 minutes on each side until puffed up and golden brown, then drain on paper towels.

Dust with powdered sugar and serve immediately.

Allow to cool slightly on a wire rack if not served immediately.