Add the pasta, broccoli, olive oil, salt, pepper, garlic, tomato sauce, milk, and broth to a large pot. Cover and bring to a full, rolling boil. Stir and reduce the heat to medium low. Simmer covered for 10-15 minutes, stirring occasionally. Cook until there is 1/2 to1 inch of liquid left in the bottom of the pot. *NOTE: Keep an eye on the pot in the beginning of the cooking process because milk tends to boil over easily.

Remove the pasta from the heat and stir in the mushrooms and the parmesan. Let the pasta rest for 3-5 minutes before serving. The remaining liquid will absorb into the pasta and the mushrooms will soften.