Prepare the Fruit Filling:
Preheat oven to 375°F.
In a large bowl, combine mixed berries, 1/4 cup sugar, and cornstarch. Toss until berries are evenly coated.
Add lemon juice and mix again.
Transfer berry mixture to a 2-quart baking dish (8x8 inch square or 9-inch round). Spread in an even layer.
Bake uncovered for 15 minutes (or 20 minutes if using very juicy berries like strawberries). Berries should start softening and juices should begin bubbling.
Make the Biscuit Topping:
While fruit bakes, whisk together flour, 1/3 cup sugar, baking powder, and salt in a medium bowl. Set aside.
Melt butter in a microwave-safe bowl until quite hot, almost sizzling.
Pour cold buttermilk into the hot melted butter all at once. Whisk immediately. Mixture will look curdled and lumpy - this is correct.
Add vanilla extract to the buttermilk mixture.
Pour buttermilk mixture into flour mixture. Stir gently just until combined. Batter will be thick and slightly lumpy. Don't overmix.
Assemble and Bake:
Remove baking dish with pre-baked berries from oven. Fruit should be bubbling around the edges.
Drop 8-10 spoonfuls of biscuit batter over the hot fruit filling. It's fine if some fruit peeks through.
Return dish to oven. Bake for 25 minutes or until biscuits are golden brown and a toothpick inserted into a biscuit comes out clean.
Let cobbler cool for at least 10 minutes before serving to allow filling to thicken further.
Serve warm with vanilla ice cream or whipped cream.