In a medium saucepan, melt the unsalted butter. Then add the flour, stirring constantly until the flour is cooked out.
Let the dough cool for around five minutes. Add the eggs one at a time, beating well after each addition.
The dough should become smooth, elastic, and pipeable.
Transfer the dough into a piping bag fitted with a star-shaped nozzle, or use a zip-top bag with the corner snipped off. Press out any excess air and set aside.
Fill a heavy-based pot with vegetable oil and heat it to 180–190°C. Carefully pipe strips of dough into the hot oil, cutting them to the desired length. Fry a few at a time for 2–4 minutes per side, or until golden and crisp. Remove with a slotted spoon and drain on paper towels.
To prepare the chocolate sauce, heat the heavy cream in a small saucepan over medium heat until it just begins to simmer. Remove from the heat and pour over the chocolate chips in a bowl, stirring until smooth.
In a shallow dish, mix the caster sugar and ground cinnamon. Roll the hot churros in the cinnamon sugar mixture until evenly coated. Serve whilst still warm.