Add cherries, ¼ cup granulated sugar, and ¼ cup (60 ml) of water to a medium sauce pan. Cook over medium heat, stirring occasionally until cherries are softened and a syrup has formed in the bottom of the pan, about 6-8 minutes. Remove from heat, and allow cherries to cool to room temperature. Transfer to a small bowl, cover, and refrigerate for later.
Fill a large bowl with ice to use later as an ice bath. Set aside.
Add heavy cream and whole milk to a heavy bottom pot. Cook over medium heat, stirring occasionally until it begins to steam around 160°F (71°C).
Meanwhile mix the remaining 1 cup sugar, cornstarch, and salt with a fork until no lumps remain and everything is well incorporated.
Once the cream and milk begin to steam, slowly add in sugar mixture in small batches, whisking continuously. Continue to cook over medium heat, whisking constantly, for an additional 2-3 minutes until the mixture has slightly thickened. You can check this by scooping a bit of the liquid up with a spoon and testing the thickness. Make sure the ice cream base does not boil at any point.
Transfer mixture to a heatproof bowl and cool in an ice bath until mixture has stopped steaming. Press a piece of plastic wrap over the mixture to prevent a skin from forming on top. Chill the ice cream base until it reaches around 40-42°F (4-5°C), or up to overnight.
Pour the mixture into an ice cream maker and process for about 20-25 minutes, or according to the manufacturer's directions. About two minutes before the ice cream is done churning, add cooked cherries and syrup a tablespoon at a time until well incorporated.
The ice cream will be on the soft side but can be eaten right away or put into the freezer to "cure" or harden up for a couple of hours. Store in an airtight container in the freezer for up to two weeks.