Make the cornstarch slurry by combining cornstarch and 2 tablespoons of milk in a small bowl. Stir until the cornstarch dissolves and set aside.
Fill a large bowl with ice water and place a 1-gallon Ziploc bag inside.
Combine the bubblegum, milk, and heavy cream in a blender. Blend on high until the bubblegum pieces are pureed into the milk. Pour the mixture into a medium saucepan, add the sugar, pinch of salt, and bring to a simmer over medium/high heat. Do not let the mixture boil over. Reduce the heat to low and add the cornstarch slurry. Whisking the entire time, cook the mixture until thickened, about 3-5 minutes.
Remove from heat and pour into Ziploc bag. Seal the bag and submerge it in the ice bath. Allow the mixture to cool completely, adding more ice as needed.
Once the mixture has cooled, place a cheesecloth over a fine mesh strainer and strain the mixture at least 3-4 times, washing out the cheesecloth each time. The cheesecloth will be sticky from the gum. Discard the solids.
Pour the mixture into an ice cream maker and freeze according to manufacturer’s instructions.