Boil a large pot of water and cook fettuccine according to directions on package. Drain and place in a serving bowl.
While fettuccine is cooking, add broccoli to a pot of boiling water and cook until tender, about 4 minutes. Drain and place broccoli in a food processor or blender with the basil, oil. Parmesan cheese, pine nuts, and garlic; process until finely chopped. Keeping machine running, use the feed tube on top and add the broth until smooth. Pour over fettuccine in bowl and mix well.