In a large mixing bowl, sift together the flour, granulated sugar, baking powder, and salt until well combined.
In a separate bowl, whisk together the milk, eggs, melted butter, and vanilla extract until smooth.
Gradually pour the wet ingredients into the dry mixture, stirring until a dough forms. The dough should be slightly sticky but manageable.
Cover the dough with plastic wrap and let it rest in the refrigerator for at least 1 hour (or up to overnight) to allow it to rise slightly.
Heat vegetable oil in a deep fryer or a large pot to 350°F (175°C).
On a floured surface, roll out the chilled dough to about 1/4-inch thickness. Use a sharp knife or pizza cutter to cut the dough into squares, approximately 2 inches by 2 inches.
Carefully drop a few squares of dough into the hot oil, being cautious not to overcrowd the pot. Fry until golden brown on one side, about 2-3 minutes, then flip and fry for another 2-3 minutes.
Remove the beignets from the oil using a slotted spoon and drain them on paper towels.
While still warm, dust generously with powdered sugar.
Notes
Allow the dough to rest for best results.
Keyword beignets, dessert, fried dough, New Orleans