Heat olive oil in a large Dutch oven or heavy pot over medium heat; cook and stir onions for 5 minutes. Add garlic and cook, stirring occasionally, until onions are translucent, about 5 minutes more.
Mix petite diced tomatoes, diced tomatoes, white wine, tomato paste, oregano, salt, sugar, black pepper, red pepper flakes, and bay leaves into onion mixture; reduce heat to low, cover Dutch oven, and simmer, stirring occasionally, until flavors blend, about 1 hour.
Remove Dutch oven from heat. Add 1/2 cup Pecorino-Romano cheese, basil, and parsley into into sauce; stir until cheese melts, about 5 minutes. Discard bay leaves. Sprinkle remaining cheese over sauce when serving.