Heat butter and oil in a large saucepan over medium. Stir in carrot, onion, and garlic.
Add ground beef, and cook until it turns from pink to brown, about 5 minutes.
Add tomatoes and their liquid, crushing them with the back of a large spoon. Stir in milk, bay leaf, thyme, nutmeg, 1/2 teaspoon salt, and 1/8 teaspoon pepper. Simmer 20 minutes.
Meanwhile, in a large pot of boiling salted water, cook fettuccine until al dente according to package instructions, about 12 minutes. Reserve about 1/2 cup of the cooking water; drain fettuccine, and return to the warm pot.
Add meat sauce, and toss.
Add pasta water as needed if the sauce seems dry. To serve, sprinkle with Parmesan.