Make sure you freeze the inner bowl of your ice cream maker for at least 24 hours prior to making this ice cream.
In a medium bowl, mash the berries together using a fork. Taste to determine the bitterness. Set aside.
In a medium or large saucepan, heat the coconut milk and sugar together over medium-high heat until sugar dissolves. Remove from heat and pour into a heat-proof glass container. Refrigerate to cool.
Once the coconut milk sugar mixture is cool, pour into the bowl of your ice cream maker. Slowly add the mashed berries. Churn according to your ice cream maker's manufacturer instructions (mine is done in 20-25 minutes). Using a spatula, scrape the ice cream into a freezer-safe container and freeze for at least 2 hours.
When ready to serve, remove from the freezer and let sit at room temperature for about 10 minutes for easier scooping.
This dairy-free ice cream will stay fresh in the freezer for up to 3 months.