Ingredients
1 stick unsalted butter
1 tablespoon plus 1 cup sugar
1 teaspoon kosher salt
1 1/4 cups unbleached all-purpose flour
4 to 5 large eggs, room temperature
1 cup heavy cream
5 ounces semisweet chocolate, finely chopped (1 cup)
1 teaspoon pure vanilla extract
2 teaspoons ground cinnamon
Vegetable, peanut, or safflower oil, for frying (about 8 cups)
Vegetable-oil cooking spray
Preparation
Combine butter, 1 tablespoon sugar, salt, and 1 cup water in a medium saucepan; bring to a boil. Remove from heat; stir in flour. Return to medium-high heat and cook, stirring constantly, until mixture pulls away from sides and a film forms on bottom of pan, 2 to 3 minutes.
Transfer mixture to the bowl of an electric mixer fitted with the paddle attachment. Beat on low speed until slightly cooled, about 1 minute. Increase speed to medium and add 4 eggs, 1 at a time, beating until a soft peak forms when you touch batter and pull your finger away. (If a peak does not form, lightly beat remaining egg, and mix into batter, a little at a time, until it does.) Transfer mixture to a piping bag fitted with a closed star tip (such as Ateco #9824).
Heat cream in a small pot over medium-high heat until bubbling around edges, about 2 minutes. Pour over chocolate in a heatproof bowl. Let stand 5 minutes, then whisk until smooth. Whisk vanilla and 1 teaspoon cinnamon into sauce.
Pour oil into a large, deep, heavy pot, such as a Dutch oven, until it reaches 2 inches up side, leaving about 2 1/2 inches headroom. Clip a deep-fry thermometer to pot and heat oil over medium to 350 degrees to 360 degrees. Cut 20 four-inch squares of parchment. Spray two baking sheets with oil. Arrange parchment pieces in a single layer on them; spray parchment.
Pipe 2 1/2-inch ribbon-shaped loops onto parchment squares. Working in batches of 3 so as not to crowd pot, carefully drop parchment with dough into hot oil, removing parchment immediately with tongs as each is added, and cook, flipping a few times, until puffed and golden brown, 6 to 8 minutes total, maintaining oil temperature between 350 degrees and 360 degrees at all times. Transfer to wire racks; let cool 10 minutes. Meanwhile, stir together remaining 1 cup sugar and 1 teaspoon cinnamon. While still slightly warm, toss churros in cinnamon sugar and serve immediately, with chocolate sauce alongside.