Activate the yeast: In a large bowl, mix warm milk, yeast, and a teaspoon of sugar. Let it sit for 5–10 minutes until foamy.
Mix the dough: Add the remaining sugar, eggs, vanilla, and butter to the yeast mixture. Gradually add flour and salt. Mix until a soft dough forms.
Knead the dough: Turn onto a floured surface and knead for 5–7 minutes until smooth and elastic.
Let it rise: Place the dough in a greased bowl, cover, and let it rise for about 1 hour or until doubled in size.
Shape the beignets: Roll out the dough to ¼-inch thickness. Cut into 2-inch squares.
Heat the oil: In a deep fryer or pot, heat oil to 350°F (175°C).
Fry the beignets: Carefully drop a few pieces at a time into the hot oil. Fry for about 1 minute per side until golden brown.
Drain and dust: Remove beignets with a slotted spoon and place them on a wire rack. Dust generously with powdered sugar while warm.