Heat a large sauté pan over medium heat. Add butter and carrots, celery and onions to the pan and sauté until the veggies are soft and begin to stick to the bottom of the pan, about 10 minutes.
Add the ground beef and pork to the pan and cook while breaking up the meat into fine crumbles. Cook until the meat is mostly browned throughout and then drain the excess fat.
Next, add the tomato paste and garlic, stir to combine and cook for 2-3 minutes.
Add the red wine to deglaze the pan, being sure to scrap the bottom of the pan to get up any stuck on bits. Allow the wine to cook off, about 5 minutes.
Add the milk, stir and bring to simmer. Allow everything to simmer until the milk has mostly evaporated, about 10 minutes.
Next, add the crushed tomatoes, bay leaves, thyme, oregano, red pepper flakes, nutmeg, salt and black pepper. Mix everything to combine, bring to a gentle simmer and cook for at least 20 minutes.
In the final minutes of cooking, cook the gnocchi according to the package instructions. Drain the gnocchi, add it to the bolognese sauce and toss to coat the gnocchi in sauce. Serve immediately with a healthy sprinkle of parmesan cheese.