Heat oil in a Dutch oven over medium-high heat. Cook and stir green bell pepper, yellow bell pepper, onion, and garlic in hot oil until tender, 5 to 7 minutes. Season the mixture with salt and pepper.
Stir tomatoes, wine, 1/4 cup parsley, basil, oregano, and red pepper flakes into the bell pepper mixture; bring to a boil, reduce heat to low, and put a cover on the Dutch oven. Cook, stirring occasionally, until the tomatoes break down, about 2 hours.
Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water until nearly cooked through, about 10 minutes; drain.
Stir drained pasta and cooked shrimp into the tomato sauce; cook until the pasta is cooked completely through yet firm to the bite, 2 to 3 minutes more. Serve with remaining parsley and Pecorino-Romano cheese.
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