Add the oil and butter to a large pan over medium heat. Then, add the onion and stir to coat with the oils. Cook until translucent.
Add the chopped celery and carrot. Then, cook for another 2 minutes while stirring.
Add in the ground beef, then cook and crumble the meat until it is fully browned.
Pour in the milk. Stir frequently while it simmers, until it has completely bubbled away. Then, repeat this process with the beef broth.
Add the tomatoes and stir well. Once the mixture begins to bubble, reduce heat to a slow simmer. Cook uncovered for 3 hours, stirring from time to time.
While the sauce is cooking, it may begin to dry out. Add ½ cup water to keep the sauce from sticking, only as necessary. At the end, no water should be left and the fat should separate from the sauce.
Add four quarts of water to a large pot and set over high heat. Add salt and bring to a boil. Cook pasta for 8-10 minutes, until al dente. Drain pasta.
Toss the Bolognese with freshly cooked pasta, then taste and add salt and pepper as desired. Serve with freshly grated parmesan to top.
