Heat the oil in a large, deep skillet over medium heat. Once it's hot, add the beef and cook, breaking it up, until it's browned throughout. Then drain any excess grease and add the onion to the skillet. Once the onion softens up, add the garlic and cook another minute or so, until fragrant. Stir in the crushed tomatoes, brown sugar, basil, salt and pepper, then lower the heat and let it simmer while you start cooking the pasta.

Preheat the oven to 375°F. Grease a 9x13" baking pan and set it aside. Cook the spaghetti until al dente in a large pot of salted water. When it's ready, drain it and return it to the pot. In a small bowl, beat the eggs, melted butter and grated parmesan cheese together. Then pour it over the drained pasta and toss to fully coat. Place the shredded mozzarella, parmesan and white cheddar in a bowl and toss together to integrate it all together.