Bring the water, butter, and 1 tablespoon sugar to a simmer in a saucepan. Stir in the flour, baking powder, and a pinch of salt all at once.
Cook, stirring firmly, until the dough pulls away from the sides and forms a smooth ball, about 2 minutes. Cool for 5 minutes, then transfer to a piping bag fitted with a star tip.
Fry and Coat:
Heat the oil to 350 F in a deep skillet or Dutch oven. Pipe 4-inch lengths of dough into the oil, snipping with kitchen scissors.
Fry in batches until golden and crisp, 3 to 4 minutes, turning once. Drain on a rack.
Mix the coating sugar and cinnamon. Toss the warm churros in the mixture.
Make the Chocolate and Serve:
Whisk the milk, cornstarch, and sugar in a small saucepan. Cook over medium heat until steaming and lightly thickened.
Remove from the heat, add the chocolate, and stir until smooth. Serve warm with the churros.
Notes
Use a star tip for crisp ridges.
Keep oil temperature steady for even frying.
Serve the churros immediately for the best texture.