In a large bowl, whisk together the flour, sugar, baking powder, salt, and nutmeg.
In another bowl, beat the eggs and then add the milk and vanilla extract. Mix well.
Pour the wet ingredients into the dry ingredients and stir until just combined. The batter will be thick and slightly lumpy.
Heat about 2 inches of vegetable oil in a deep pan or skillet over medium heat. You can test if the oil is ready by dropping a small amount of batter into the oil; it should float and sizzle.
Using a spoon or cookie scoop, drop spoonfuls of batter into the hot oil. Do not overcrowd the pan.
Fry the beignets until they are golden brown and puffed, about 2-3 minutes per side. Use a slotted spoon to remove them from the oil and drain on paper towels.
Dust the hot beignets with powdered sugar before serving.
Enjoy your meal!