In a medium saucepan, combine whole milk (or half-and-half), heavy cream, sugar, medium-ground coffee, and kosher salt. Heat over medium until the mixture is warm but not boiling, about 5–7 minutes. Remove from heat and let it steep for 15 minutes.

While the coffee mixture is steeping, whisk together the egg yolks and any remaining sugar in a medium bowl until pale and slightly thickened, about 2–3 minutes.

Set up an ice bath by filling a large bowl with ice and water. Nest a smaller bowl or strainer on top of the ice.

Gradually pour the warm coffee mixture into the beaten egg yolks while continuously whisking to temper the eggs. Return the mixture to the saucepan over medium heat, stirring constantly until it thickens enough to coat the back of the spatula, about 5–10 minutes.

Pour the custard through the strainer into the bowl set over the ice bath. Press the mixture with a spatula to extract flavor while leaving coffee grounds behind.

Stir the strained custard until it cools to room temperature, around 10–15 minutes. Transfer it to an airtight container and refrigerate for at least 4 hours.

After chilling, pour your custard into an ice cream maker and churn according to the manufacturer’s instructions for 20–30 minutes.

When the ice cream is nearly finished churning, drizzle in cajeta and gently fold in the chocolate chips.

Transfer the layered ice cream to an airtight container and freeze for an additional 4 hours or until firm.