Cook pasta in salted water for 4 minutes (ladle out a cup of the starchy pasta water and set aside) and then drain.
Leave pasta in colander and melt 2 tablespoons butter in the the pot. Add the mushrooms and saute for 2 minutes over medium heat. Empty into a bowl and set aside.
Melt 2 more tablespoons and add the garlic, cooking for 30 seconds. Whisk in the whipping cream, half and half, and tomato sauce. Add the pasta and then bring to a boil over medium heat. Boil for 4-5 minutes (add the broccoli for the last 2-3 minutes), stirring occasionally.
When pasta is al dente, remove from heat and stir in the Parmesan cheese. Add a little of the reserved pasta water at a time to thin sauce to desired consistency. Salt and pepper to taste.