Making Vanilla French Beignets is straightforward if you follow these steps:

1. Combine Dry Ingredients: In a large bowl, whisk together the flour, sugar, baking powder, and salt.

2. Mix Wet Ingredients: In another bowl, mix the milk, egg, melted butter, and vanilla extract until well incorporated.

3. Combine Mixtures: Pour the wet mixture into the dry ingredients. Stir until a soft dough forms. Be sure not to overmix; a few lumps are fine.

4. Knead the Dough: On a floured surface, gently knead the dough for about 30 seconds until it comes together. Form it into a ball.

5. Let Dough Rest: Cover the bowl with a damp cloth and let it rest for about 1 hour at room temperature. This allows the dough to rise.

6. Roll Out the Dough: After resting, transfer the dough to a floured surface and roll it out to about 1/4-inch thickness.

7. Cut Shapes: Use a sharp knife or a pizza cutter to cut the dough into squares, approximately 2 inches by 2 inches.

8. Heat Oil: In a deep pot or heavy skillet, heat oil to 350°F (175°C). Make sure there is enough oil to submerge the beignets.

9. Fry Beignets: Carefully place a few pieces of dough into the hot oil, ensuring not to overcrowd the pot. Fry for 5-6 minutes, turning them occasionally until golden brown on all sides.

10. Drain and Dust: Using a slotted spoon, remove the beignets and place them on paper towels to drain excess oil. While still warm, dust generously with powdered sugar.

11. Repeat: Continue frying the remaining dough squares until all have been cooked.