Bring a large pot of well-salted water to a boil. Cook the pasta according to package directions until al dente. Drain, transfer to a large bowl, and toss with 1 tsp. of the oil.

Dry the pot, and heat the remaining 5 Tbs. oil until shimmering. Reduce the heat to low. Add the garlic and pepper flakes, and cook, stirring often, until aromatic and soft, about 2 minutes. Add the tomatoes, 1 tsp. salt, and 1/2 tsp. black pepper. Increase the heat to medium-high, and cook, stirring, until the tomatoes are very soft, about 5 minutes. Return the pasta to the pot, and stir until just heated through, about 2 minutes. Add the basil, pine nuts, oregano, and cheese, and toss well. Serve with more cheese at the table.