To make the salted caramel sauce, heat 1 cup granulated sugar in a medium saucepan over medium heat, stirring constantly until it melts and turns a deep amber color.

Carefully whisk in the cubed butter until melted, then slowly pour in the heavy cream while whisking vigorously (be careful as the mixture will bubble up).

Remove the sauce from heat, stir in the sea salt, and let it cool slightly while you prepare the churros.

In a separate saucepan, combine water, 1/2 cup butter, 2 tablespoons sugar, and salt, bringing the mixture to a rolling boil over medium-high heat.

Reduce the heat to low, add the flour and cocoa powder at once, and stir vigorously with a wooden spoon until the dough forms a ball and pulls away from the sides of the pan.

Transfer the dough to a mixing bowl and let it cool for about 5 minutes, then beat in the eggs one at a time until the mixture is smooth and glossy.

Heat the vegetable oil in a deep pot or Dutch oven to 375°F (190°C), using a thermometer to ensure the correct temperature.

Transfer the chocolate dough into a piping bag fitted with a large star tip.

Carefully pipe 4 to 5-inch strips of dough into the hot oil, using scissors to cut the dough at the nozzle.

Fry the churros in batches for about 3 to 4 minutes per side, or until they are firm and crispy.

Remove the churros with a slotted spoon and drain them briefly on a paper towel-lined plate.

In a shallow dish, mix the coating sugar, ground cinnamon, and cayenne pepper together.

Toss the warm churros in the spiced sugar mixture until they are generously coated on all sides.

Serve the crispy chocolate churros immediately alongside the warm salted caramel sauce for dipping.