Preheat your oven to 375°F (190°C). Lightly grease an 8x8 inch baking dish or a 9-inch pie plate.

Prepare the fruit filling: In a large bowl, gently toss the mixed berries, sliced peaches, 1/2 cup sugar, cornstarch, and lemon juice together until the fruit is evenly coated. Pour the mixture into the prepared baking dish.

Prepare the topping: In a separate medium bowl, whisk together the flour, 1/4 cup sugar, baking powder, and salt. Cut in the cold butter cubes using a pastry blender or your fingertips until the mixture resembles coarse crumbs.

Stir in the milk and vanilla extract until just combined; be careful not to overmix the dough. Drop spoonfuls of the topping evenly over the fruit filling in the baking dish, leaving small gaps between scoops.

Sprinkle the top evenly with 1 tablespoon of turbinado sugar for extra crunch. Bake for 35 to 40 minutes, or until the topping is golden brown and the fruit filling is bubbling thickly.

Remove the cobbler from the oven and let it cool slightly (about 15 minutes) before serving warm, topped generously with scoops of vanilla ice cream.