In a large bowl, whisk together the flour, sugar, baking powder, and salt.
In another bowl, beat the eggs and mix in the milk and vanilla.
Pour the wet ingredients into the dry ingredients and mix until just combined.
Stir in the melted butter until smooth.
Heat oil in a deep fryer or heavy pot to 350°F (175°C).
Using a spoon or small scoop, drop batter into the hot oil.
Fry until golden brown, about 2-3 minutes per side.
Remove beignets and drain on paper towels.
Dust with powdered sugar while warm.
Serve immediately and enjoy!