Bring a pot of salted water to boil and cook pasta about 10 minutes. Add frozen broccoli cuts and cook 5 more minutes.
While cooking pasta, warm oil in large skillet over medium heat. Add sausage and cook, breaking it up with a patatoe masher, until brown (about 9 minutes). Add garlic and cook about 2 more minutes.
Reserve 1 cup of liquid from pasta. Drain pasta and broccoli and return to pot. Pour sausage into pasta with the cup of liquid you set aside. Season with salt & pepper. Toss and cover over low for about 5 minutes. (Check and add a little water if necessary)