Cook the spaghetti according to the package directions. Drain and return the pasta to the pot.
Meanwhile, heat the oil in a large saucepan over medium heat. Add the mushrooms and cook, stirring occasionally, for 6 minutes.
Add the garlic, beef, salt, and pepper. Cook until no trace of pink remains, about 5 minutes.
Spoon off and discard any fat. Add the tomatoes and their juices and bring to a boil.
Reduce heat and stir in the cream and ¾ cup of the Parmesan. Simmer until the sauce has thickened slightly, about 3 minutes.
Add the sauce to the pasta and toss. Divide among plates and sprinkle with the remaining Parmesan and the parsley.