In a small bowl, combine the warm milk and active dry yeast. Stir gently and let it sit for about 5-10 minutes until frothy.
In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, and salt. Create a well in the center and add the yeast mixture, eggs, melted butter, and vanilla extract. Stir until a sticky dough forms.
Transfer the dough onto a lightly floured surface and knead for about 5-7 minutes until smooth and elastic.
Place the dough in a greased bowl, cover it with a clean kitchen towel, and let it rise in a warm place for about 1-1.5 hours, or until it has doubled in size.
Once the dough has risen, punch it down to release any air bubbles. Transfer it back to the floured surface and roll it out to about ½-inch thickness. Use a pizza cutter or a sharp knife to cut the dough into squares, roughly 2×2 inches.
Heat vegetable oil in a large pot or deep skillet to 350°F (175°C).
Fry 3–4 beignets at a time, being careful not to overcrowd the pot. Fry for 1–2 minutes on each side, until golden brown. Use a slotted spoon to remove them and place them on a paper towel-lined plate to drain excess oil.
Generously dust the warm beignets with powdered sugar and serve immediately.
