In a small bowl, mix 2 tablespoons of milk with the cornstarch to make a slurry.
In a medium-sized saucepan, combine the remaining milk, cream, sugar, corn syrup, salt, and coffee grounds.
Heat the mixture over medium heat, stirring occasionally until the sugar dissolves and the mixture comes to a simmer.
Remove the saucepan from heat and let it steep for 15 minutes.
Strain the mixture through a fine-mesh strainer into a clean saucepan.
Reheat the mixture over medium heat and gradually add the cornstarch slurry, whisking constantly.
Bring the mixture to a boil and let it cook for 1 minute, stirring constantly.
Remove the saucepan from heat and let the mixture cool to room temperature.
Cover the saucepan and chill it in the refrigerator for at least 2 hours, or until it is thoroughly chilled.
Churn the mixture in an ice cream maker according to the manufacturer's instructions.
Transfer the ice cream to a container and freeze for at least 4 hours, or until firm.