Stir coconut milk, coconut cream, corn syrup, and sugar together in a saucepan. Cook on medium-low heat until sugar dissolves, about 5 minutes. Add coffee powder, cocoa, and vanilla extract; whisk until fully combined.
Remove 2 tablespoons of the coconut mixture. Whisk with cornstarch in a bowl to make a slurry. Pour back into the coconut mixture. Stir until slurry is evenly distributed.
Refrigerate until completely chilled, 3 hours to overnight.
Freeze per manufacturer's directions, 8 hours to overnight.
For other flavors, omit the coffee and cocoa, and add other ingredients - mint chocolate chip, maple cinnamon, peanut butter... Use your imagination! The base is neutral enough to use a variety of favors.
Per Serving: 324 calories;27.8 g fat;
20.6 g carbohydrates;
3.1 g protein;
0 mg cholesterol;
9 mg sodium.