Step 1: In a medium saucepan, combine the heavy cream, whole milk, and half of the granulated sugar. Add the instant espresso powder (or strong brewed coffee/espresso, or whole coffee beans if using). Heat over medium heat, stirring occasionally, until the mixture is hot and steamy but not boiling. If using whole beans, remove from heat, cover, and let steep for 15-20 minutes, then strain out the beans before proceeding.
Step 2: In a separate bowl, whisk together the egg yolks and the remaining granulated sugar until light in color and slightly thickened.
Step 3: Slowly ladle about half a cup of the hot cream mixture into the egg yolk mixture, whisking constantly. Continue adding hot cream, a little at a time, until about half of the hot cream has been incorporated into the egg yolks.
Step 4: Pour the tempered egg yolk mixture back into the saucepan with the remaining hot cream. Return the saucepan to medium-low heat. Cook, stirring constantly with a wooden spoon or heat-proof spatula, until the custard thickens enough to coat the back of the spoon (it should leave a clear trail when you run your finger across it). Do not let it boil.
Step 5: Immediately remove the custard from the heat and strain it through a fine-mesh sieve into a clean bowl. Stir in the vanilla extract.
Step 6: Place plastic wrap directly on the surface of the custard to prevent a skin from forming, then refrigerate for at least 4 hours, or preferably overnight, until thoroughly chilled.
Step 7: Once the custard is completely chilled, pour it into your ice cream maker and churn according to the manufacturer’s instructions. This usually takes 20-30 minutes, resulting in a soft-serve consistency.
Step 8: Transfer the soft ice cream mixture to an airtight container. For the best firm, scoopable ice cream, freeze for another 4-6 hours until hardened.