In a large skillet over medium heat, add the butter and oil.
Once the butter has melted and the oil is hot, add onion, celery, and carrot. Cook for 5-7 minutes, or until softened.
Add ground beef, salt, pepper, and nutmeg. Cook, stirring occasionally and breaking up the meat as you go, for about 8-10 minutes, or until the meat is no longer pink.
Pour in the milk and bring the mixture to a simmer. Continue simmering, stirring occasionally, for 8-10 minutes, or until the milk has mostly evaporated.
Increase heat to medium-high and pour in the beef broth. Cook, stirring occasionally for about 8-10 minutes, or until the broth has mostly evaporated.
Stir in the crushed tomatoes. Bring the mixture to a simmer again, stirring occasionally, for 30-35 minutes, or until thickened. Near the end of your sauce cook time, prepare your pasta.
In a large pot, cook the pasta al dente according to the package directions. Using tongs, transfer the pasta directly from the pot to the bolognese sauce, tossing to coat.
Add reserved pasta water, 1 tablespoon at a time, as necessary to reach your desired consistency. (You may not need to add the pasta water.)
Serve immediately, garnished with parsley and shaved parmesan cheese as desired.