Step 1

Combine blackberries, sugar, and lemon zest in the bowl of a food processor; process until mixture is pureed. Let sit for 10 minutes.

Step 2

Strain the seeds through a fine mesh sieve and return puree to the food processor. Add cream, milk, and vanilla extract. Pulse until mixture is whipped, about 30 seconds.

Step 3

Pour mixture into an ice cream maker and freeze according to manufacturer's instructions, about 20 minutes. Transfer to an airtight container and freeze until firm, 2 hours to overnight.