To prepare the churros:

1. Heat 1 inch of oil in a large skillet to a temperature of 360 degrees F.
2. In a large saucepan, heat the water, butter and salt to a boil. Stir in the flour. Continue to stir until the dough forms into a ball, about 1 minute. Remove from heat.
3. In a small bowl, beat the eggs until smooth. Pour the egg mixture into the saucepan. Stir until well combined.
4. Transfer the dough to a piping tube fitted with a large star tip. Squeeze 4-inch strips of the churro dough into the hot oil.
5. Working in batches, fry the churros until golden brown, about 2 minutes per side. Transfer fried churros to a paper towel-lined plate to drain.
6. In a shallow pie plate, combine the cinnamon and sugar. Roll each churro into the cinnamon-sugar mixture until well coated.

To prepare the chocolate dipping sauce:

1. In a small saucepan over low heat, combine the chocolate and 1/2 cup of the milk.
2. In a small bowl, dissolve the cornstarch in the remaining 1/2 cup of milk. Whisk the cornstarch mixture into the chocolate mixture. Stir in the sugar until well combined.
3. Whisk continuously until the chocolate mixture thickens, about 5 minutes. Remove from heat, and whisk vigorously until smooth.
4. Transfer the sauce to individual dipping cups, and serve with churros.