For the tomato filling: Preheat the oven to 350 degrees F.
Heat 3 tablespoons of olive oil in a large skillet over medium-high heat. Add the onion and cook, stirring occasionally, until soft and lightly golden, about 5 minutes. Add the garlic, basil sprigs and crushed red pepper and cook, stirring occasionally for about 2 minutes, then add the chopped tomatoes and 1 1/2 teaspoons salt. Bring to a simmer and cook until the tomatoes just begin to soften, 4 to 5 minutes. Remove from heat and discard the basil sprigs. Add the cherry tomatoes and flour and gently stir to evenly coat. Check for seasoning and add more salt, if necessary. Transfer the tomato filling to a 2-quart baking dish and dot with the mozzarella balls. Drizzle with the remaining tablespoon of olive oil.
For the biscuit topping: In a medium bowl, whisk together the cornmeal, flour, baking powder, sugar, 1/2 teaspoon salt and pepper to taste in a medium bowl. Add the butter and use a pastry cutter or your fingers to rub the butter into the flour until you achieve pea-sized pieces. Make a well in the center of the flour and add the buttermilk, Parmesan and basil and gently combine with a fork until a sticky dough forms; take care not to overwork the dough.
Drop heaping tablespoons of the dough on top of the tomato filling. Brush with olive oil. Place the cobbler on a baking sheet and bake until the top is golden and the filling bubbly, about 1 hour. Remove and let rest for 15 minutes. Serve warm.
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