In a large mixing bowl, combine 1 cup of warm milk (around 110°F) and 2 teaspoons of active dry yeast. Allow the yeast to bloom for about 5-7 minutes until it becomes frothy. Then, mix in 2 beaten eggs, ¼ cup of granulated sugar, ¼ cup of melted unsalted butter, and 2 teaspoons of vanilla extract until well blended.

Gradually add 4 cups of all-purpose flour to the wet mixture, stirring until a soft dough forms. Once incorporated, transfer the dough to a floured surface and knead it for about 5-10 minutes until it becomes smooth and elastic.

Place the kneaded dough into a lightly greased bowl, covering it with a clean kitchen towel or plastic wrap. Set it in a warm, draft-free area to rise until it has doubled in size, approximately 1 hour.

Once the dough has risen, turn it out onto a floured surface and gently roll it out to about ½ inch thickness. Using a sharp knife or pizza cutter, cut the dough into 2-inch squares.

In a deep, heavy-bottomed pot, heat about 2 inches of oil over medium heat until it reaches 350°F. Use a thermometer to ensure the oil is at the right temperature.

Carefully lower a few beignet squares into the hot oil, ensuring not to overcrowd the pot. Fry each batch for about 2-3 minutes per side or until they turn a beautiful golden brown.

Once golden, remove the beignets from the oil and place them on a paper towel-lined plate to drain and cool slightly. While still warm, generously dust them with powdered sugar.