Add the oil and butter to a large, deep skillet over medium heat. Once melted, add the onion, carrot, and celery and cook for 5 minutes, stirring occasionally.
Add the beef, turn the heat up to medium-high, and cook until browned- about 5 minutes. Stir occasionally with a wooden spoon to break up the meat.
Add the wine and cook until it’s mostly evaporated off, about 5 minutes- stirring occasionally.
Stir in the crushed tomatoes, salt, black pepper, and bay leaves. Cook on low (uncovered) until thickened- about 30 minutes- stirring frequently.
Stir in the milk. Cook (uncovered) until the sauce is quite thick- about 15 more minutes, stirring constantly.
Stir in the shredded Parmesan. Stir in the cooked pasta, or add pasta to serving bowls with sauce spooned on top.
Sprinkle the parsley on top and serve along with more Parmesan to sprinkle on top.
Notes
If you serve this as 6 servings, they will not be large servings. Serve a small amount of pasta and a scoop of the bolognese sauce.