Preheat oven to 400 degrees F (200 degrees C).

If you're using frozen fruit, thaw and drain it before proceeding. Combine fruit in an ungreased 2-quart casserole dish. Mix the cornstarch and 2/3 cup sugar, and toss with fruit mixture. Dot with 2 tablespoons butter and set aside.

Sift the flour, baking powder, sugar, and salt into a bowl. Stir in the oats, lemon zest, and cinnamon. Cut in 1/4 cup butter until it's the size of small peas. Stir in milk to form a stiff batter. Spoon dollops of cobbler batter over the fruit in the casserole dish; the batter may not entirely cover the fruit.

Bake in the preheated oven until the fruit is bubbling and the topping is golden brown, about 30 minutes. Allow to cool about 15 minutes. Serve warm.