In a medium saucepan, stir together heavy cream, whole milk, 3/4 cup sugar, instant coffee granules, and cinnamon sticks over medium-high heat. Bring the mixture to a low boil.

In a small bowl, combine egg yolks and remaining 1/4 cup sugar. Whisk together until smooth. Slowly add 1/4 cup of the heavy cream mixture to the egg mixture, whisking quickly to incorporate. Once well combined, add the egg mixture to the heavy cream mixture. Cook over medium heat until the mixture is thick and coats the back of a metal spoon.

Remove from heat. Strain into a medium bowl and cover with plastic wrap, making sure the plastic wrap touches the surface of the custard to prevent a film from forming. Chill completely.

Add the custard mixture to your ice cream machine. Churn the ice cream according to the manufacturer’s instructions. Chill overnight or for a minimum of 7-8 hours before serving.