Heat oil over medium-high heat in a large saucepan.
Add mushrooms, garlic, and onion and sauté for 10 minutes.
Add tomatoes, tomato paste, oregano, salt, and pepper, and bring mixture to a boil.
Reduce heat to medium and simmer for about 12 minutes.
Remove from heat and add milk.
Meanwhile, cook pasta according to package directions, then drain and return to pot.
Add mushroom mixture, tossing to coat.
Sprinkle with cheese and serve immediately.