In a saucepan over medium heat, combine the blackberries, sugar, and lemon juice. Cook, stirring occasionally, until the berries break down and the mixture thickens, about 10-15 minutes. Remove from heat and let cool completely.
Prepare the Cobbler Pieces:
Preheat your oven to 375°F (190°C). In a mixing bowl, combine the flour, sugar, and salt. Cut in the cold butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs. Stir in the milk until just combined.
Spread the dough in a thin layer on a baking dish and bake for 12-15 minutes, or until golden brown. Allow to cool, then break into small pieces.
Make the Ice Cream Base:
In a mixing bowl, whisk together the heavy cream, whole milk, sugar, and vanilla extract until the sugar is dissolved.
Churn the Ice Cream:
Pour the ice cream base into your ice cream maker and churn according to the manufacturer’s instructions until it reaches a soft-serve consistency.
Assemble the Ice Cream:
Gently fold the blackberry compote and cobbler pieces into the churned ice cream. Transfer the mixture to a lidded container and freeze for at least 4 hours, or until firm.
Notes
For a richer flavor, roast the blackberries in the oven with a bit of sugar before making the compote.