In a large mixing bowl, combine the all-purpose flour, granulated sugar, baking powder, salt, and ground nutmeg. Whisk together until the mixture is well mixed and there are no lumps.
In another bowl, crack the egg and beat it lightly. Add the whole milk, vanilla extract, and melted butter to the egg, whisking until the mixture is smooth and thoroughly combined.
Gradually incorporate the wet mixture into the dry ingredients. Mix gently until the two are just combined; it’s okay if the batter remains slightly lumpy, as overmixing can make the beignets tough.
Cover the bowl with a clean kitchen towel and let the dough rest at room temperature for approximately 30 minutes. This helps the dough to rise slightly and improves the texture.
In a deep fryer or heavy-bottomed pot, heat about 2 inches of vegetable oil to 350°F (175°C). A candy thermometer can help you maintain the perfect temperature.
While the oil is heating, lightly dust a clean work surface with flour. Turn the rested dough onto the floured surface and gently roll it out to about 1/2 inch thickness.
Use a sharp knife or pizza cutter to cut the rolled dough into 2-inch squares, making sure to create even pieces for uniform cooking.
Carefully drop the squares of dough into the hot oil, frying only a few at a time to prevent overcrowding. Fry for about 2-3 minutes on each side, or until they achieve a beautiful golden brown color.
Once golden, use a slotted spoon to remove the beignets from the hot oil and place them on a plate lined with paper towels to absorb excess oil.
While the beignets are still warm, dust them generously with powdered sugar for a sweet finish before serving.
Notes
Serve the beignets in a charming basket lined with parchment paper. For an extra treat, pair them with a side of whipped cream or a rich chocolate sauce for dipping!