Preheat the oven to 375°F (190°C). In a mixing bowl, combine blackberries, peaches, sugar, cornstarch, vanilla extract, and lemon juice. Toss gently to coat the fruit evenly.

Transfer the fruit mixture to a greased baking dish, spreading it out evenly.

In a separate bowl, whisk together flour, baking powder, salt, and sugar.

Cut in the cold butter using a pastry cutter or fork until the mixture resembles coarse crumbs.

Stir in the milk until just combined. Do not overmix.

Drop spoonfuls of the biscuit dough over the fruit filling, leaving some gaps for the fruit to show through.

Bake in the preheated oven for 30-35 minutes or until the biscuits are golden brown and the filling is bubbly.

Let cool slightly before serving. Enjoy warm with ice cream if desired.