In a saucepan, combine the heavy cream, whole milk, and sugar. Heat over medium heat until the sugar is dissolved and the mixture is hot but not boiling.

In a separate bowl, whisk the egg yolks. Gradually add a small amount of the hot cream mixture to the yolks, whisking constantly to temper them.

Pour the tempered yolks back into the saucepan and cook over low heat, stirring constantly, until the mixture thickens enough to coat the back of a spoon.

Remove from heat and stir in the instant coffee granules and vanilla extract until fully dissolved.

Let the mixture cool to room temperature, then refrigerate until completely chilled, about 2 hours.

Once the mixture is chilled, pour it into an ice cream maker and churn according to the manufacturer's instructions until it reaches a soft-serve consistency.

Transfer the ice cream to an airtight container and freeze for at least 2 hours to firm up.