In a small bowl, pour just enough hot water over the porcini mushrooms to cover. Let soften while beginning the sauce.
In a large, heavy pot warm the olive oil over medium heat. Add the onion, carrot, and garlic and cook until softened. Add the pancetta, prosciutto, and tomato paste and stir until the tomato paste is dissolved.
Add the mushrooms and their soaking water, the beef broth, and the jarred marinara sauce. Simmer for 15 minutes. Let cool then ladle into jars.