Preheat oven to 375°F (190°C). Grease a 12-cup muffin tin.
In a large bowl, combine the berries, sugar, cornstarch, and lemon juice. Gently toss to combine.
Divide the berry mixture evenly among the muffin cups.
In a separate bowl, combine the flour, sugar, and salt for the crumble topping.
Cut in the cold butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs.
Sprinkle the crumble topping evenly over the berry filling in each muffin cup.
Bake for 25-30 minutes, or until the topping is golden brown and the berry filling is bubbly.
Let the cobbler cups cool slightly before serving.