Measure out the 2 cups of whole milk. In a small bowl, whisk 2 tablespoons of the measured milk with the cornstarch to form a slurry. Set aside.
In a large bowl, whisk together the mascarpone and salt to form a smooth paste. Set aside.
In a heavy-bottomed, 4-quart saucepan, combine the remaining milk, heavy cream, corn kernels, sugar, and corn syrup. Turn heat to medium-high and bring mixture to a roiling boil; the mixture will foam a lot. Boil for 4 minutes, stirring frequently with a heatproof spatula, making sure to scrape the bottom and edges of the pan to prevent scorching or boiling over.
Remove from heat and strain the mixture through a fine-mesh strainer, pressing on the corn kernels to release liquid. Discard the corn.
Return the liquid mixture to the saucepan. Gradually whisk in the cornstarch slurry, then bring the mixture to a boil again over medium-high heat. Stirring constantly with the heatproof spatula, cook for about 1 minute, until the mixture thickens slightly.
Remove from heat and whisk a small amount of the mixture into the mascarpone. Once smooth, slowly whisk the rest of the liquid into the mascarpone.
Prepare an ice bath in a large bowl. Pour the ice cream mixture into a 1-gallon Ziploc bag, carefully press out excess air, and seal the bag tightly. Place the bag in the ice bath and chill for 15–30 minutes, replenishing ice as necessary, until the ice cream base is cold.
Set up the ice cream maker in a cool spot in the house. Pour the ice cream base into the frozen canister and churn according to machine directions. The base is ready when it reaches 21° (or colder) and looks creamy and thick.
Transfer one third of the ice cream to a shallow, plastic storage container with a lid. Drizzle ⅓ of the blueberry swirl over the top. Repeat with two more layers, ending with blueberry swirl. Do not stir the blueberry swirl into the ice cream. Cover tightly and immediately transfer to the coldest part of the freezer (usually the back). Freeze until very firm, at least 4 hours.