In a large bowl, whisk together the flour, sugar, baking powder, and salt.
In another bowl, combine the milk, eggs, and melted butter.
Gradually add the wet ingredients to the dry ingredients, mixing until a soft dough forms.
Turn the dough onto a floured surface and knead gently for 2-3 minutes.
Roll out the dough to about 1/4 inch thickness.
Cut into squares (about 2-inch pieces).
Heat the vegetable oil in a deep fryer or large pot to 350°F (175°C).
Fry the beignets in batches, turning until golden brown, about 2-3 minutes per side.
Remove with a slotted spoon and drain on paper towels.
Dust generously with powdered sugar before serving.