Add cherries, ¼ cup granulated sugar, and ¼ cup 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.
Fill a large bowl with ice to use later as an ice bath. Set aside. Add heavy whipping 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).
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 mixture has slightly thickened.
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.
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.