Combine sugar and ground nutmeg in a shallow dish.

Combine flour, water, butter, orange peel, and salt in a medium saucepan.

Stir constantly over low heat until a dough ball forms and leaves a film on the bottom of the pan (about 2 minutes).

Remove the saucepan from the heat.

Transfer the dough to a food processor.

Blend in the egg until the dough is smooth.

Heat vegetable oil in a deep skillet to 350°F (175°C).

Spoon the batter into a pastry bag fitted with a 1/4-inch star tip.

Working in batches, pipe the batter into the hot oil in approximately 4-inch-long ribbons.

Fry until golden brown, turning occasionally, for about 3 minutes.

Transfer the fried churros to paper towels to drain excess oil.

While still warm, turn the churros in the sugar and nutmeg mixture to coat evenly.

Serve immediately and enjoy.