Bring a large pot of salted water to a boil. When boiling, add the pasta and cook according to package directions. When the pasta is al dente, strain in a colander and return the pasta to the large pot. Cover to keep warm.
While the pasta is cooking, bring another saucepan filled 2/3 full of salted water to a boil. Add the cauliflower and cook until crisp-tender, about 5 minutes. Using a slotted spoon, transfer the cauliflower to the pot with the pasta.and cover to keep warm.
Meanwhile, in a skillet over medium-high heat, crumble the Italian sausage and cook until browned and cooked through, about 4 minutes. Add the pepperoni and cook for 2 minutes, just to release a little of the fat. Transfer the meats to the pot with the pasta and veggies and cover to keep warm. Add 1 1/2 tablespoons of the olive oil to the hot pan along with the onions and bell peppers and cook until the vegetables are soft, about 4 minutes. Add the garlic, basil, oregano, and crushed red pepper and cook for 1 minute, stirring. Using a spoon, transfer the sauteed onion mixture to the pasta pot.
Add the remaining olive oil, the cubed mozzarella cheese, green and black olives, and parsley to the pot and, using 2 large wooden spoons, toss to thoroughly combine. Serve the pasta in a large bowl for everyone to help themselves. Pass the cheese at the table.
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