Preheat the oven to 350 degrees.
Place a large pot of salted water on the stove over medium-high heat. Place the tomatoes inside a large baking dish. Toss the tomatoes with 4 tablespoons of the olive oil, garlic, vinegar, red pepper flakes, salt, and pepper. Roast until the tomatoes are tender, stirring occasionally, about 40-45 minutes. Remove from the oven and toss with the basil, parsley, and oregano.
Once the water comes to a boil, cook the rotini according to the package directions or until the pasta is al dente. Drain and return to the pot. Toss the pasta with the olive oil, add the tomatoes with their juices, and cook until pasta and tomatoes are heated through, about 1-2 minutes.
Add the ricotta cheese and cook, stirring, until the ricotta melts, about 1 minute. Remove from the heat, divide into 6 portions, top with the pine nuts and pecorino cheese, if using, and enjoy.