Combine the cocoa, coffee and sugar in a small saucepan. Bring to a boil over medium heat, stirring to dissolve the sugar, and boil for 30 seconds. Remove from the heat, add the chocolate and let stand for 5 minutes. Stir the syrup until smooth and set aside.

Mix about 2 tablespoons of the milk with the cornstarch in a small bowl to make a slurry.

Whisk the cream cheese, warm chocolate syrup and salt together in a medium bowl until smooth.

Fill a large bowl with ice and cold water.

Combine the remaining milk, the cream, sugar, corn syrup, cinnamon stick and cayenne in a 4-quart saucepan and bring to a rolling boil over medium-high heat. Boil for 4 minutes. Remove from the heat and gradually whisk in the cornstarch slurry. Bring the mixture back to a boil over medium-high heat and cook, stirring with a heatproof spatula, until slightly thickened, about 1 minute. Remove from the heat.

Gradually whisk the hot milk mixture into the cream cheese mixture until very smooth. Pour the mixture into a 1-gallon Ziploc freezer bag and submerge the sealed bag in the ice bath. Let stand, adding more ice as needed, until cold, about 30 minutes.

Remove cinnamon stick before pouring the ice cream base into the frozen canister. Spin until thick and creamy. Just before the ice cream is done, tip in the cacao nibs so they will get stirred through.

Pack the ice cream into a storage container, press a sheet of parchment directly against the surface and seal with an airtight lid. Freeze in the coldest part of your freezer until firm, at least 4 hours.