In the bowl of a stand mixer, add the flour, sugar, yeast, salt, vanilla extract, and oil.

Mix everything together.

Crack the eggs into the warm milk and beat well with a whisk or fork.

Add the milk and eggs to the mixer bowl.

Knead the dough for 10 minutes.

Shape the dough into a ball, cover with a kitchen towel or plastic wrap, and let rise for 1 hour.

Gently deflate the dough without kneading, shape it into a log, and divide into 8 pieces.

Shape each piece into a ball, flatten with your palm, and place on a kitchen towel dusted with flour.

Cover the dough with a towel and let rise again.

Drain the beignets on paper towels.

Serve the beignets plain or filled, with a hot or cold beverage.