Preheat the oven to 325 degrees . Arrange a rack on top of a baking sheet. Place the tomatoes cut side up on the rack and roast for 20 minutes to slump the tomatoes and tart up their sweetness. While still warm, toss the tomatoes with the parsley, basil, onion and mint. Dress the salad with about 2 tablespoons EVOO; season with salt.
Meanwhile, bring a large pot of water to a boil, salt it, add the pasta and cook to just shy of al dente. Drain, reserving 1 cup of the pasta cooking water.
While the pasta cooks, in a large skillet, heat about 1/4 cup EVOO , the garlic and some pepper. Cook until fragrant, 3 to 4 minutes; discard the garlic.
Add the pasta and three-quarters of the reserved cooking water to the skillet. Add 3/4 cup cheese and toss to form a saucy coating, about 2 minutes (adding a splash more cooking water or more cheese as needed). Serve the pasta in shallow bowls and top with the tomato salad for mixing in as you eat. Pass the remaining cheese at the table.