In a medium bowl, combine 1 cup of warm milk, 2 1/4 teaspoons of active dry yeast, and a pinch of sugar. Stir gently and let it sit for about 5 to 10 minutes until the mixture is foamy on top.

Once the yeast mixture is foamy, add 1/4 cup of granulated sugar, 1 large egg, 1 teaspoon of vanilla extract, 1/2 teaspoon of salt, and 1/4 cup of melted unsalted butter. Whisk until well combined.

Gradually add 3 1/2 to 4 cups of all-purpose flour to the wet ingredients, mixing until a soft dough forms.

Transfer the dough to a lightly floured surface and knead for about 5 to 7 minutes, until smooth and elastic.

Place the kneaded dough in a greased bowl, cover it, and let it rise in a warm area for 1 to 1.5 hours until it doubles in size.

After rising, punch the dough down gently and roll it out to about 1/4-inch thickness. Cut into 2 to 3-inch squares.

In a large pot, heat sufficient vegetable oil to 350°F (175°C).

Carefully drop a few squares of dough into the hot oil, frying for 1 to 2 minutes on each side until golden brown.

Using a slotted spoon, remove the fried beignets and place on paper towels to drain. Dust with powdered sugar while warm.

Serve the Vanilla French Beignets warm, ideally with coffee.