Begin by cooking the spaghetti according to the package instructions. To season the water, add a generous amount of salt, a pinch of dried oregano, and a tablespoon of olive oil to the boiling pot before adding the pasta. This not only flavors the pasta but also prevents it from sticking together.
Before draining, reserve 2 cups of the starchy pasta water to use in the sauce. This liquid will help bind and thicken the sauce while enhancing the texture of the final dish.
While the pasta cooks, prepare the sauce. In a food processor, combine the tomato paste and fresh tomatoes. Slowly pour in the reserved pasta water—starting with one cup—and blend until the consistency is rich and smooth but not overly thin. Add more water as needed.
In a large skillet, heat a splash of olive oil over medium heat. Stir in the garlic paste and cook until fragrant, about 30 seconds. Add the cooked ground beef to the skillet, followed by the tomato sauce mixture. Stir in the sugar, crushed red pepper, and dried oregano. Simmer the sauce for several minutes until slightly thickened and heated through.
Add the cooked spaghetti directly to the meat sauce without rinsing it. Toss thoroughly to coat each strand with the sauce, allowing the starch on the pasta to help the sauce cling.
Before serving, stir in the shredded cheddar for a hint of creaminess and top with freshly grated Parmesan. Serve hot, with extra red pepper flakes or herbs if desired.