Heat the oil in a large skillet over medium-high heat. Add the beef and cook, crumbling with a spoon, until no longer pink, 5 to 7 minutes.
Add the wine and cook until the liquid has nearly evaporated, 4 to 6 minutes.
Add the milk, tomatoes, nutmeg, 1 teaspoon salt, and ½ teaspoon pepper and bring to a boil.
Reduce heat and simmer until the sauce begins to thicken, 15 to 20 minutes. Stir in the parsley.
Meanwhile, cook the pasta according to the package directions. Drain, return it to the pot, and toss with the sauce. Serve with the Parmesan.