In a large skillet over medium heat, melt the butter and heat the olive oil until shimmering.

Add the diced onion, celery, and carrot. Cook, stirring occasionally, for 5 to 7 minutes, or until the vegetables are soft and fragrant.

Add the ground beef, kosher salt, black pepper, and nutmeg. Cook, breaking up the beef with a wooden spoon or spatula, for 8 to 10 minutes, or until the meat is fully browned and no longer pink.

Pour in the whole milk and bring the mixture to a gentle simmer. Continue simmering for 8 to 10 minutes, stirring occasionally, until the milk has mostly evaporated.

Increase the heat to medium-high. Add the beef broth and simmer for another 8 to 10 minutes, stirring occasionally, until the broth has mostly reduced.

Stir in the crushed tomatoes. Bring the sauce to a simmer, then reduce heat to low and cook for 30 to 35 minutes, stirring occasionally, until the sauce thickens and develops deep flavor.

Using tongs, transfer the cooked pasta directly into the skillet with the sauce. Toss gently to coat the noodles evenly with the bolognese.

If the sauce is too thick, add reserved pasta water 1 tablespoon at a time, until the sauce reaches your desired consistency. (You may not need all of it.)

Serve immediately, topped with shaved parmesan cheese and chopped fresh parsley if using.