Transfer the blackberries to a food processor. Add the vanilla and salt, and roughly chop the mixture to your desired consistency. (More finely chopped fruit will freeze more evenly.)
Transfer the blackberry mixture back into a bowl, and add the milk. Stir to combine.
Assemble and turn on ice cream maker. Pour ice cream mixture into the ice cream maker and let it freeze (about 15-20 minutes). Serve immediately.
If you want the ice cream to freeze harder, transfer the ice cream to a freezer-safe container and freeze for at least 1 hour. Let ice cream sit at room temperature for 5-10 minutes before serving.