Start by making the churro dough. In a medium saucepan, combine water, butter, and salt. Bring to a boil over medium heat.
Once boiling, reduce the heat to low and stir in the flour until the mixture forms a ball and pulls away from the sides of the pan.
Remove from heat and let the dough cool for a few minutes. Then, add the eggs one at a time, fully incorporating each before adding the next.
Transfer the dough into a piping bag fitted with a large star tip.
Heat the vegetable oil in a large pot or deep fryer to 375°F (190°C). Pipe strips of dough into the hot oil and fry until golden brown, about 2-3 minutes per side.
Mix the sugar and cinnamon in a shallow dish. Drain the churros on paper towels and then toss them in the sugar mixture while still warm.
For the chocolate chili sauce, heat the heavy cream in a small saucepan until it begins to simmer.
Remove from heat and add the chopped dark chocolate, chili powder, and cayenne pepper. Let sit for one minute, then stir until smooth.
Serve the warm churros with the chocolate chili sauce for dipping.