First, make sure you have placed your ice cream maker base bowl in the freezer for at least 24 hours before making the ice cream. It needs to be completely frozen, otherwise your ice cream will not turn out.
Shake the cans of coconut milk to incorporate the layers. Open the cans of coconut milk. Measure 1/2 cup and set this aside in a small bowl. Pour the remaining coconut milk into a 2-quart saucepan set over medium-high heat.
Add the sweetener and salt to the saucepan.
Warm the coconut milk mixture, stirring occasionally, until the sweetener has completely dissolved, which takes 1-2 minutes.
Meanwhile, whisk the cornstarch into the bowl that has the 1/2 cup coconut milk until the cornstarch has completely dissolved into the milk. Then add this mixture to the coconut milk mixture in the sauce pan and whisk gently.
Cook this mixture in the saucepan and stir constantly until it becomes thickened, about 6-8 minutes. Do not allow the mixture to come to a boil.
Remove from heat and stir in the vanilla. This is your ice cream base.
Pour ice cream base into a shallow pan and allow to cool at room temperature before covering and cooling in the freezer for at least 4 hours.
While the base is cooling, make the cherry sauce: Mash the cherries down in a small saucepan, sprinkle in the sugar, and bring to a low boil. Reduce the heat to simmer and cook for about 5 minutes, or until the berries start to lose their shape and become juicy. Remove from heat, transfer to a bowl, and allow to cool at room temperature for 30 minutes. Blend the mixture in a food processor or blender for just a few seconds until a thick sauce forms. Set aside.
Once the ice cream base has been frozen for at least 4 hours, begin to churn it according to your ice cream maker's instructions. At about 10-15 minutes in, when you can see the base has thickened to a soft-serve ice cream consistency, slowly ladle the strawberry sauce into the ice cream maker while it's running. Allow the sauce to blend into the ice cream base.
After about 5 minutes, slowly add in the chocolate chips while the ice cream maker is still running, and churn until your ice cream has reached your desired consistency. For me, this took about 5 more minutes after adding the chips.
Spread the ice cream into a large loaf pan and freeze for a few more hours or overnight, until the ice cream has firmed up completely.
When you're ready to serve the ice cream, take it out of the freezer and let it sit at room temperature for about 5 minutes before serving.