Add the oil, onion, celery, and carrots to a large pot over medium-high heat. Sauté for about 10 minutes.
Stir in the garlic and mushrooms, and continue sautéing for another 5-7 minutes or until the mushrooms release their water and cook down a bit.
Add in the beef and pork and break the meats up with your spoon. Continue cooking, stirring fairly often, until the meats change color (about 10 minutes).
Stir in the Dijon mustard, Worcestershire sauce, Italian seasoning, and oregano.
Stir in the tomato paste, diced tomatoes, tomato sauce, beef broth, and wine.
Increase the heat to high and bring the sauce to a gentle boil. Give it a good stir, then reduce the heat and simmer (you want a steady bubble but not a furious boil) for 45 minutes, pot covered with the lid slightly ajar. I recommend checking on it periodically. This sauce should cook fairly slowly so the flavors infuse, but you don't want the liquid to get too low. Add a splash more beef broth or wine if this happens.
Stir in the cream and give the sauce a taste and season with salt & pepper as needed.
Serve over spaghetti and then top with parmesan cheese and chopped fresh basil and/or parsley.