Bring a large pot of salted water to a boil.
Heat a second large pot over medium-high heat. Add the beef, 1/2 teaspoon salt and a few grinds of pepper and cook, stirring to break the meat up, until browned, about 4 minutes. Add the onions, bell peppers, garlic and a generous pinch of salt and pepper and cook, stirring occasionally, until tender, about 10 minutes. Stir in the crushed and diced tomatoes, sugar and oregano and bring to a boil. Reduce the heat to simmer and cook, stirring occasionally, until thickened, about 30 minutes.
Meanwhile, cook the spaghetti for 2 minutes less than the time indicated in the package directions. Strain well. Preheat the oven to 350 degrees F.
Cover the bottom of a 13-by-9-by-2-inch pan with a third of the sauce. Add half the pasta and a third of the Cheddar; repeat the layers and add the last of the sauce; reserve the last of the Cheddar.
Bake for 30 minutes. Top with the remaining Cheddar and continue baking until it melts and the sauce bubbles, about 5 more minutes. Let cool in the dish for at least 10 minutes. Garnish with the parsley before cutting into squares.
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