Prepare the pasta according to the package instructions.
While the pasta is cooking, heat the oil in a large pot over medium heat. Add the onion and cook, stirring, for 30 seconds. Add the garlic and cook, stirring, for 30 seconds. Add the bell pepper and carrot and cook until the vegetables are softened and golden-brown, stirring occasionally, about 5 minutes.
Increase the heat to high and add the ground pork, using a spatula or spoon to break up the meat. Cook until the pork is browned, about 5 minutes. Add the crushed tomatoes, balsamic vinegar, kosher salt, and sugar and bring to a boil, about 5 minutes. Reduce the heat to low, cover, and simmer, stirring occasionally, for 45 minutes.
Serve over the hot cooked pasta.