Set up your ice cream machine (most devices require the bowl to be in the freezer for 24 hours before making ice cream).
In a small saucepan over medium-low heat, combine the sugar, heavy cream, milk, cinnamon stick, ground cinnamon, cayenne, vanilla extract, and salt and bring it to just below simmering. Before it simmers, stir and turn off the heat.
In a large bowl, whisk your egg yolks. Temper the eggs by slowly pouring in a small amount of the warm milk mixture while mixing continuously. Once 1 cup of the milk has been slowly incorporated, add all of the milk mixture.
Pour the mixture through a fine mesh strainer back into the saucepan that contained the milk. Heat the custard over medium heat until it reaches 180 degrees or thickens enough to coat the back of a spoon.
Strain the mixture again into a bowl and chill for at least 4 hours in the fridge.
Pour the mixture into your ice cream machine and follow the manufacturer’s instructions.
Place the ice cream into a freezer-safe, lidded container and freeze for at least 4 hours.