2 (15-ounce) cans full-fat coconut milk
1/2 cup agave nectar
1/4 teaspoon kosher salt
2 tablespoons cornstarch
1 vanilla bean, split
1 dry pint (2 cups) strawberries, hulled and quartered
1/4 cup natural cane sugar
Shake the cans of coconut milk thoroughly before opening. Scoop out 1/2 cup of coconut milk and set it aside. Combine the remaining coconut milk, agave, and salt in a saucepan. Bring to a simmer over medium-low heat until all of the ingredients combine smoothly and the mixture is uniformly warmed, about 2 minutes.
In a small bowl, whisk remaining 1/2 cup coconut milk with the cornstarch until well-combined. Stir into the warm coconut milk base. Scrape the vanilla bean into the mixture and slip in the pod as well. Cook over medium heat until the mixture has thickened enough to coat the back of a spoon, 6 to 8 minutes. Do not to allow the mixture to boil.
Remove from the heat, discard the vanilla bean pod, and pour the coconut base into a separate bowl. Cool on the counter for 30 minutes, then cover with plastic wrap and chill in the refrigerator for 4 to 5 hours — you need the base to be very cold before you process it in the ice cream machine.
While the base is cooling, make the strawberry sauce: Mash the strawberries down in a medium 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 the heat, transfer to a bowl, and cool on the counter for 30 minutes. Once slightly cool, blend in a food processor or blender, or with an immersion blender, for just a few seconds until a thick sauce forms. Set aside.
Churn the coconut ice cream base in your ice cream machine following the manufacturer’s instructions. When thickened to a soft-serve ice cream consistency, slowly ladle the strawberry sauce into the ice cream maker as it runs so the sauce gets incorporated into the ice cream base. Spread the ice cream into a large loaf pan (or pie pan) and freeze for a few more hours (or overnight) until the ice cream has firmed up completely.