In a large mixing bowl, combine the whole milk and whipping cream. Whisk together until well blended.
Add the cream cheese to the milk and cream mixture. Using an electric mixer, beat until the cream cheese is completely incorporated and the mixture is smooth.
In a separate bowl, whisk together the instant espresso, unsweetened cocoa powder, and granulated sugar. Gradually add this dry mixture to the wet ingredients, stirring continuously until everything is well combined.
Stir in the kosher salt and vanilla extract, mixing until fully incorporated.
Cover the bowl with plastic wrap and refrigerate the mixture for at least 2 hours, or until it is completely chilled.
Once chilled, pour the mixture into your ice cream maker and churn according to the manufacturer’s instructions. This usually takes about 20-25 minutes.
During the last few minutes of churning, add the dark chocolate espresso bits or chocolate chips to the mixture, allowing them to mix in evenly.
Transfer the churned ice cream to a freezer-safe container and smooth the top. Place a piece of plastic wrap directly on the surface of the ice cream to prevent ice crystals from forming, then seal with a lid. Freeze for at least 4 hours, or until firm.