Bring a medium pot of water to a boil, add the pasta and cook according to package directions; drain, reserving 1/2 cup of the pasta water. Return the pasta to the pot.
Meanwhile, heat the olive oil in a large nonstick skillet over medium-high heat. Add the sopressata and cook, stirring, until blistered and the oil turns reddish, about 3 minutes. Add the artichoke hearts, Spanish olives, Kalamata olives and roasted red pepper and stir to coat. Add the tomatoes, basil leaves, olive brine and reserved pasta water. Bring to a simmer and cook until most of the water evaporates and the sauce thickens slightly, 8 to 10 minutes.
Add the sauce and mozzarella to the pasta in the pot and stir to combine. Divide among 4 bowls and sprinkle with more basil. Serve with bread.
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