In a small saucepan, heat the heavy cream until it's just beginning to simmer. Remove from heat and add the chopped chocolate. Let it sit for a minute, then stir until smooth. Mix in the vanilla extract.
In a medium saucepan, combine water, 2 tablespoons sugar, salt, and butter. Bring to a boil over medium heat. Once the butter is melted, reduce the heat to low and add the flour. Stir vigorously until the mixture forms a ball, about 1 minute. Remove from heat and let it cool for a few minutes. Once cooled, add the eggs, one at a time, mixing well after each addition.
In a large skillet or deep fryer, heat the oil to 375°F (190°C).
While the oil is heating, mix together the granulated sugar and cinnamon in a shallow dish. Set aside.
Transfer the churro dough to a piping bag fitted with a large star nozzle. Carefully pipe 3-4 inch long strips of dough directly into the hot oil, using scissors to snip off the ends. Fry the churros, turning them once, until golden brown, about 2-3 minutes per side. Using a slotted spoon, transfer the churros to a paper towel-lined plate to drain for a minute, then roll them in the cinnamon sugar while still warm.
Serve churros warm with the chocolate dipping sauce on the side.