In a large mixing bowl, whisk together the flour, granulated sugar, baking powder, and salt until well combined.
In a separate bowl, mix the milk, eggs, vanilla extract, and melted butter until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix; a few lumps are okay.
Cover the bowl with plastic wrap and let the batter rest for about 30 minutes at room temperature.
In a deep skillet or pot, heat about 2 inches of vegetable oil over medium heat until it reaches 350°F.
Using a spoon or a small cookie scoop, drop spoonfuls of the batter into the hot oil, being careful not to overcrowd the pan. Fry for about 2-3 minutes on each side or until golden brown.
Use a slotted spoon to transfer the beignets to a paper towel-lined plate to drain excess oil.
Dust the warm beignets generously with powdered sugar before serving.