While the pasta boils, heat the oil or broth in a large, roomy, deep skillet. Add the mushrooms and sausage slices. Cook, stirring often, for 7-10 minutes, or until the mushrooms have released their juices and are completely tender. Add the broccoli (if fresh) to the skillet, cover, and allow it to steam cook for 3-4 minutes, or until crisp-tender. If using defrosted, add the broccoli to the skillet and heat through.