Add cherries, ¼ cup (50 grams) granulated sugar, and water to a medium saucepan. Cook over medium heat, stirring occasionally until cherries are softened and a thickened syrup has formed in the bottom of the pan, about 10 - 15 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. Place an empty bowl on top of the ice. Set aside.
Add milk, heavy cream, and vanilla 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 (200 grams), 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 - 4 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.
Place a fine mesh strainer over the empty bowl on top of the ice bath. Strain ice cream base. Chill ice cream base until it 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 according to the manufacturer's directions, about 25 - 30 minutes. During the last 5 minutes, add cooked cherries and syrup a tablespoon at a time, then allow the machine to continue churning until thickened.
The ice cream will be on the soft side. Transfer to an airtight container and place in the freezer to "cure" or harden up for 6 - 8 hours. Store in the freezer for up to two weeks.