Position rack in center of oven and preheat to 350 degrees F.
In a large, glass baking dish, toss the tomatoes with the oil, garlic, vinegar, salt, red pepper flakes, and pepper. Roast until the tomatoes are tender, stirring occasionally, 40 to 45 minutes. Remove from the oven and add the basil, parsley, and oregano. Stir well.
Bring a large pot of salted water to a boil and cook the pasta until al dente, about 7 minutes. Drain and return to pot. Toss with the extra-virgin olive oil. Add the tomatoes and pan juices and cook over low heat until hot, 1 to 2 minutes. Add the ricotta salata cheese and stir until mostly melted, about 1 minute. Remove from the heat and transfer to a large serving bowl.
Toss with the pine nuts and Pecorino cheese. Garnish with additional herbs, as desired, and serve immediately.