In a mixing bowl, whisk together flour, sugar, baking powder, and salt until well combined.

In another bowl, combine milk, eggs, vanilla extract, and melted butter. Whisk until thoroughly mixed.

Gradually pour the wet mixture into the dry ingredients, stirring until a dough forms.

Turn the dough out onto a floured surface and roll it to about 1/2-inch thick.

Cut the rolled dough into squares or circles.

In a deep fryer or large pot, heat oil to 350°F (175°C) for frying.

Fry the beignets in batches, cooking until golden brown, about 2-3 minutes per side.

Remove them from the oil and let them drain on paper towels.

While warm, dust the beignets generously with powdered sugar before serving.