Mix 50 g sugar and 2 tsp cinnamon on a shallow plate, line a sheet pan with paper towels, and fit a piping bag with a 1 cm / 1/2-inch star tip. Chop the chocolate finely and put it in a heatproof bowl.

Bring 240 ml water, 2 tbsp oil, 1 tbsp sugar and 1/2 tsp salt to a rolling boil in a 2-quart / 1.9 L saucepan. Take it off the heat, add all 150 g flour at once, and stir hard with a wooden spoon for about 1 minute, until the dough forms a smooth ball that pulls away from the sides.

Scrape the dough into a bowl and let it cool for 5 minutes, until you can touch it comfortably. Hot dough is too soft to hold its ridges.

While the dough cools, warm 180 ml milk and 60 ml cream in a 1.5-quart / 1.4 L saucepan over medium heat for about 3 minutes, until steaming with small bubbles at the edge. Pour it over the chopped chocolate and wait 1 minute. Whisk in 1/2 tsp cinnamon, 1/4 tsp cayenne, a pinch of salt and 1 tsp vanilla until glossy, then cover to keep warm.

Pour 1 L oil into a 26 cm / 10-inch Dutch oven so it's about 5 cm / 2 inches deep. Heat over medium for about 8 minutes, until a thermometer reads 175 C / 350 F. Spoon the cooled dough into the piping bag.

Pipe 4 lengths of dough into the oil, cutting each at 12 cm / 5 inches with kitchen scissors held close to the surface. Fry for 3 to 4 minutes, turning once or twice, until deep golden brown with crisp ridges. Cut the first churro open to check that the center is set and fluffy.

Lift the churros out with a spider skimmer, drain on the towel-lined pan for 10 seconds, then roll them in the cinnamon sugar while still hot. Wait 1 to 2 minutes for the oil to return to 175 C / 350 F, then fry the remaining dough in two more batches of 4, for 12 churros total.

Whisk the sauce, pour it into a small bowl, and serve the churros within 20 minutes of frying.