Combine water, butter, salt, and sugar in a medium sized saucepan and bring to a boil. Using a wooden spoon, stir in the flour then remove from heat. Continue to stir until the mixture begins to adhere to itself and form a ball.

Transfer the mixture to the bowl of an electric mixer then beat it for 1 or 2 minutes just to cool it down slightly.

With the mixer on slow speed, add the eggs, one at a time, beating until each addition is incorporated. Mixture should be smooth and shiny. Let the dough rest while you preheat the oil.

Pour enough oil into the pan to be a least 2 inches high. Heat to 350-375 degrees.

Meanwhile, make the chocolate sauce.

Heat 1/2 cup of the milk and the chocolate in a small sauce pan until chocolate is melted. Whisk cornstarch into the remaining 1/2 cup of milk. Bring the melted chocolate mixture to a boil then whisk in cornstarch mixture and sugar. Reduce heat to low and simmer, stirring often, until mixture is thickened, about 5 minutes. Remove from heat.

Transfer the churro dough to a pastry bag fitted with a large star tip. Grab a pair of scissors, a plate or baking pan lined with paper towels, and a bowl with the 1/2 cup of sugar and 1 teaspoon cinnamon whisked together.

Over the pot of hot oil, squeeze the churro dough to about 4 inches in length then use the scissors to cut them off into the hot oil. You should be able to cook 3-4 at a time, depending on the size of your pot. Cook churros until golden on both sides, or about 1-2 minutes per side.

Place finished churros on the paper towel to drain. When they're just cool enough to handle, roll them in the cinnamon sugar mixture. Serve warm with chocolate sauce.