In a large mixing bowl, whisk together the flour, 1/4 cup sugar, baking powder, salt, cinnamon, and nutmeg until well combined.
In a separate bowl, mix the buttermilk, egg, and melted butter until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined. The dough will be slightly sticky.
Turn the dough out onto a floured surface and gently knead it a few times until it comes together. Pat it into a rectangle about 1/2 inch thick.
Cut the dough into 2-inch squares or use a round cutter for a different shape.
In a deep pot or fryer, heat about 2 inches of vegetable oil to 350°F.
Carefully drop the beignets into the hot oil, a few at a time, and fry for about 2-3 minutes on each side or until golden brown.
Remove the beignets with a slotted spoon and drain on paper towels.
In a small bowl, mix together 1/2 cup sugar and 1 teaspoon cinnamon. While the beignets are still warm, toss them in the cinnamon sugar mixture until coated.
Serve warm and enjoy!