Churros

Chocolate Sauce: Combine cream and corn syrup in a small saucepan over medium; bring to a simmer, stirring occasionally. Remove from heat and add chocolate, paprika, and cayenne; stir until chocolate is melted. Cover to keep warm and set aside.

Churros: In a medium saucepan, combine 1 cup water, butter, granulated sugar, and salt; bring to a boil over medium-high. Remove from heat and stir in flour. Return to medium-high 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 a stand mixer fitted with the paddle attachment. Beat on low speed until slightly cooled, about 1 minute. Increase speed to medium and add eggs, one at a time, beating until each addition of egg is fully incorporated before adding the next one.

Continue to beat mixture until soft peaks form when you touch the batter and pull your finger away. Transfer mixture to a piping bag fitted with a closed star tip (such as Ateco #846). 

Pour enough oil into a large, deep, heavy pot (such as a Dutch oven) until it reaches 2 inches up the side, leaving about 2 1/2-inches of headroom. Clip a deep-fry thermometer to pot and heat oil over medium to between 350° and 360°. Working in batches, hold pastry bag a few inches from oil and pipe out a few 4-inch-long ropes of batter, snipping off dough at ends with a pair of kitchen shears. 

Fry churros, flipping once, until puffed and deep golden brown all over, about 6 minutes. Transfer to wire racks; let cool slightly then dust with confectioners' sugar. Repeat with remaining batter, adjusting oil as needed to maintain temperature. Serve churros immediately with reserved chocolate sauce on the side.