In a blender or food processor, combine the frozen strawberries, thick part of the coconut milk (about 1/3 cup), and vanilla extract. If you like your sorbet on the sweeter side, you can add a bit of maple syrup to taste. Blend until smooth and creamy. Repeat these steps with the blackberries.
Dollop small amounts of the mixture in a dish overlapping each flavor. Place the dish in the freezer.
Freeze the sorbet until it's firm enough to scoop, usually about 3-4 hours.
Once the sorbet is frozen and scoopable, it's ready to enjoy! Serve it in bowls or cones for a beautiful and refreshing dessert.