For chocolate custard base: In a 4-quart saucepan, combine milk, cream, half of sugar and cinnamon stick. Set over high heat, and cook, stirring occasionally, until mixture comes to a boil, about 5 minutes. Meanwhile, in a medium bowl, whisk yolks and remaining sugar until smooth, heavy, and pale yellow, about 30 seconds.
When cream mixture just comes to a boil, whisk, remove from heat, and, in a slow stream, pour half of cream mixture over yolk-sugar mixture, whisking constantly until blended. Return pan to stovetop over low heat. Whisking constantly, stream yolk-cream mixture back into pan.
With a wooden spoon, continue stirring until mixture registers 165 to 180 degrees on an instant-read thermometer, about 2 minutes. Do not heat above 180 degrees, or eggs in base will scramble.
Mixture should be slightly thickened and coat back of spoon, with steam rising, but not boiling. (If you blow on the back of the spoon and the mixture ripples, you’ve got the right consistency.) Remove cinnamon stick.
Remove from heat and immediately add chopped chocolate, whisking until smooth. Pour base into a clean airtight container and refrigerate for 12 to 24 hours before using.
For ice cream: Add zest, cayenne pepper, vanilla and mezcal to base. Process in an ice cream maker according to manufacturer’s instructions. Add mezcal during last 2 minutes of churning.
Scrape into an airtight storage container. Freeze for a minimum of 2 hours before serving.