Cook the pasta according to the package directions. Drain.
Meanwhile, heat 1 tablespoon of the oil in a large saucepan over medium heat. Add the garlic and cook for 1 minute.
Add the tomatoes, sugar, 1 teaspoon salt, and ⅛ teaspoon pepper. Bring to a boil. Reduce heat and simmer until slightly thickened, about 15 minutes.
Meanwhile, heat the remaining tablespoon oil in a medium skillet over medium heat. Add the onion and carrot and cook until soft, about 6 minutes.
Add the beef and ½ teaspoon salt and cook until no trace of pink remains. Stir the beef into the sauce. Fold in the parsley.
Divide the pasta among bowls, top with the sauce, and sprinkle with the Parmesan.