Stir the chopped strawberries, lemon juice, and 3 tablespoons of turbinado sugar together in a medium bowl. Use a fork for a potato masher to mash the strawberries together just a bit. Cover and set the bowl in the fridge to let the strawberries macerate while you prepare the rest of the ingredients.

Warm coconut cream, coconut milk, remaining ½ cup of sugar, corn syrup, vodka, coconut oil, and vanilla bean seeds and pod in a medium pot over medium heat, stirring occasionally. When the cream begins to simmer, remove the pot from heat. Cover and let the mixture steep for 20 minutes. Remove the bean pod and reserve it to make vanilla extract.

Meanwhile, prepare an ice bath by filling a large bowl with ice cubes and water.

Pour the cream and all but ¼ cup of the macerated strawberries into a blender or food processor and purée until smooth. Strain and reserve the remaining ¼ cup of strawberries.

Pour the puréed mixture into a large 1-gallon Ziploc bag. Seal it and submerge the mixture in the ice bath until cold, about 30 minutes.

Pour the strawberry ice cream base into the bowl of your pre-frozen ice cream maker. Follow the directions on your ice cream maker to churn the base into ice cream, until it is the consistency of soft-serve, about 15 minutes. Add the chopped chocolate and remaining ¼ cup of drained chopped strawberries and churn just until evenly incorporated throughout, 3 more minutes.

Pack the ice cream into an air-tight storage container or a metal loaf pan, pressing a sheet of parchment paper directly against the ice cream.

Freeze until firm, at least 4 hours, but preferably overnight.