In a large mixing bowl, combine warm milk, active dry yeast, and a pinch of granulated sugar. Let sit for 5-10 minutes until frothy.

Whisk in sugar, beaten egg, vanilla extract, salt, and melted butter until combined.

Gradually add flour, stirring until a soft, sticky dough forms. Knead on a floured surface for 5-7 minutes until smooth and elastic.

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

Punch down the dough, roll out to 1/4 inch thick, and cut into squares or rectangles.

Heat vegetable oil in a deep pot to 350°F (175°C).

Fry beignet squares in batches for 1-2 minutes on each side until golden brown.

Remove from oil and let drain on paper towels. Dust with powdered sugar while warm.