Heat oven to 400 F. Prick potato in several spots and bake on a cookie sheet until skin begins to crisp and potato has a little give when squeezed, about 40 minutes. (You may also cook the potato in the microwave.)
Cool until the potato is comfortable to touch. Peel off the skin.
Place peeled potato, blackberries, coconut milk, sugar, and vodka in a blender and blend until smooth.
Press blended mixture through a sieve to strain out blackberry seeds.
Churn in an ice cream maker according to the manufacturer’s instructions.