Combine cream and milk in a saucepan and heat until steaming.

Finely chop the smoked chocolate in a food processor.

Add corn syrup, salt, some of the milk mixture, and mezcal (if using) to the chocolate and process until smooth.

Pour the remaining milk mixture into a bowl, add the chocolate mixture, and whisk until smooth.

Chill the mixture in an ice bath or refrigerator for about 1 hour.

Pour the chilled mixture into an ice cream maker and churn according to the manufacturer's instructions.

Transfer the ice cream to an airtight container and freeze until firm, approximately 2 hours.

Heat oil in a Dutch oven or skillet to 360°F.

Mix cinnamon and sugar in a shallow dish.

In a saucepan, combine water, butter, salt, and sugar and heat until butter is melted.

Add flour and stir until a ball forms.

Remove from heat and add eggs one at a time, mixing well after each addition.

Transfer the mixture to a pastry bag fitted with a star tip.

Pipe 3- to 4-inch churros into the hot oil and fry until golden brown and crispy, about 5-6 minutes, turning occasionally.

Drain the churros on paper towels.

Dredge the warm churros in the cinnamon-sugar mixture.

Serve the churros with the smoked chocolate ice cream.