These churros can be piped into decorative spirals or made in the more classic baton shape. Enjoy these with our Spiced Chocolate Eggnog.
Bring water, butter, 1 tablespoon sugar, and the salt to a boil in a medium saucepan. Remove from heat, and stir in flour. Return pan to medium heat, and cook, stirring constantly with a wooden spoon, until dough forms a smooth ball, about 1 1/2 minutes. Transfer to a mixer bowl, and let cool for 3 minutes.
With mixer on medium speed, add egg, and beat until dough is smooth and shiny, about 3 minutes. (Dough will be sticky.)
Heat 2 inches of oil in a heavy-bottomed medium pot until it registers 375 degrees on a deep-fry thermometer. Mix cinnamon, a pinch of cayenne, if using, and remaining 1/4 cup sugar in a medium bowl.
Spoon dough into a pastry bag fitted with a large open-star tip. Hold pastry bag a few inches above the oil, and pipe six to eight 5-inch lengths, moving bag in circular motions while piping to create decorative shapes if desired. Cut dough with an oiled knife. Fry, turning once, until golden brown, about 2 minutes. Transfer to a paper-towel-lined baking sheet to drain, then toss in sugar mixture. Repeat with remaining dough. Serve immediately.