Cook the spaghetti according to the package directions.
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 3/4 cup of the Parmesan. Simmer until the sauce has thickened slightly, about 3 minutes.
Drain the pasta and return it to pot. Add the sauce and toss. Divide among plates and sprinkle with the remaining Parmesan and the parsley.
Tip: For a delicious, lower-calorie version of this dish, omit the cream.