Combine warm milk and 1 tablespoon granulated sugar in a large bowl, then sprinkle in active dry yeast and let it sit for 5-10 minutes until foamy.

Add the remaining granulated sugar, eggs, melted butter, and vanilla extract to the yeast mixture and whisk gently until combined.

Gradually add flour and salt to the wet ingredients, mixing until a soft, shaggy dough forms.

Turn the dough onto a lightly floured surface and knead for 5-7 minutes (or 3-4 minutes with a stand mixer) until smooth and elastic.

Lightly oil a clean bowl, place the dough in it, turn to coat, then cover and let rise in a warm place for 1.5 to 2 hours until doubled in size.

Punch down the risen dough, roll it to ½-inch thickness on a floured surface, and cut into 2-inch squares.

In a heavy-bottomed pot, heat 2-3 inches of vegetable oil to 350°F (175°C).

Carefully drop 3-4 beignet squares into the hot oil, frying for 1-2 minutes per side until golden brown and puffed up.

Transfer fried beignets to a wire rack over paper towels to drain, then liberally dust with powdered sugar while still warm.

Serve the beignets immediately for the best fresh and warm taste.