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.
Reserve some of the pasta cooking water, and add a little to the sauce if it seems too thick. The water is ideal for adjusting the consistency of the sauce, and the starch in the water helps the sauce adhere to the pasta.