While the oil heats, combine the water, butter, ¼ teaspoon of the cinnamon, and salt in a small saucepan. Bring to a boil, then reduce the heat to low.
Slowly stir in the flour until the mixture forms a ball.
Remove the saucepan from the heat and let the dough cool for 5 minutes.
Add the eggs one at a time, stirring until fully combined after each addition.
Fit a piping bag with a large star tip and fill it with the dough.
Pipe 1–2-inch strips of dough over the hot oil, cutting each strip with a knife. Work in batches to avoid overcrowding the pot.
Fry for 2–3 minutes, until golden brown.
Remove the churros with a slotted spoon and drain on a paper towel-lined plate.
Combine the sugar and remaining cinnamon in a shallow dish.
Roll the warm churros in the cinnamon-sugar mixture until coated. Serve warm.