Prepare to fry the churros by heating 1 to 1 1/2 inches oil in a deep pan to 360 degrees F.
To make churro dough, heat water, butter and salt to rolling boil in 3-quart saucepan; stir in flour. Stir vigorously over low heat until mixture forms a ball, about 1 minute; remove from the heat. Beat eggs all at once; continue beating until smooth and then add to saucepan while stirring mixture.
Spoon mixture into a piping tube with large star tip. Squeeze 4-inch strips of dough into hot oil. Fry 3 or 4 strips at a time until golden brown, turning once, about 2 minutes on each side. Drain on paper towels. Mix the sugar and cinnamon. Roll churros in the cinnamon sugar. Serve with Chocolate Dunking Sauce.
Place the chocolate and half of the milk in a pan and heat on low. When the chocolate has melted, dissolve the cornstarch in the remaining milk and whisk into the chocolate with the sugar. Cook on low heat, whisking constantly, until the chocolate is thickened, about 5 minutes. Add extra cornstarch if it does not start to thicken after 5 minutes. Remove and whisk smooth.
Pour and serve in cups for dipping churros.