Puree blackberries in a food processor for 15-20 seconds.
With a mixer, beat heavy whipping cream until thick. Pour in sweetened condensed milk, vanilla, and blackberries fold in until smooth.
Next, spoon ice cream into a freezer-safe container.
Freeze for 5-6 hours or overnight. When it is time to serve, remove the container from the freezer and let sit on the counter for 5-10 minutes before serving to soften.