In a large bowl, dissolve yeast in warm water. Let sit until foamy (about 5–10 minutes).

Stir in sugar, eggs, milk, vanilla, and half the flour. Mix until smooth.

Add remaining flour, salt, and butter. Knead into a soft dough.

Cover and let rise in a warm spot for 1–2 hours, until doubled.

Roll dough to ¼-inch thickness. Cut into 2-inch squares.

Heat oil in a deep pot to 350°F (175°C). Fry beignets in batches, turning once, until golden brown (about 1 minute per side).

Drain on paper towels and dust generously with powdered sugar.