Freeze the bowl of a 2QT ice cream maker at least 12 hours in advanced, before making the ice cream.
Add 2 cups of the chopped cherries to a large bowl with the granulated sugar and stir it together. Let it sit for about 10 minutes.
Scoop the cherries, sugar, and heavy cream into a blender and blend until the cherries are chopped up and the mixture is combined.
Stir the milk into the cream mixture. Add in the vanilla extract, almond extract, and the salt.
Pour the cherry cream mixture through a strainer to strain out the cherry skins.
Add the ice cream to a prepared ice cream maker and churn according to the ice cream makers directions, about 30 minutes.
Add the remaining 3/4 cup of cherries to a small bowl with the granulated sugar and let it sit while the ice cream is churning.
Strain the cherries through a fine mesh strainer to get the extra liquid out. Blot lightly with a paper towel.
Once the ice cream is thickened to a soft serve consistency, add in the chocolate chips and chopped cherry pieces. Let it churn for another 5 to 10 minutes until they are mixed well into the ice cream.
Serve immediately for a creamy, soft ice cream, or scoop it into a 2QT container and cover and freeze for at least 6 hours, or even better overnight.