Bring a large pot of salted water to a boil for the pasta.
Cut the salami into small cubes and set aside.
Heat the olive oil over medium heat in a large skillet. Add the onion and sauté until slightly softened, 2 minutes. Add the carrot and continue cooking for 2 to 3 minutes. Add the celery and garlic and cook until the carrots are very tender and the entire mixture is nicely caramelized, 4 to 5 minutes longer.
Add the red wine and tomato paste and stir until smooth. Add the salami, cover and simmer gently for 5 minutes. Season to taste with salt and pepper. Add the tomatoes, reduce the heat to low, cover and keep warm, stirring occasionally while the pasta cooks.
Cook and drain the rigatoni according to package directions. Add the parsley to the sauce and combine with the pasta. To serve, plate individual servings and top with grated Parmigiano-Reggiano.