1. Cut carrot, and the green and yellow zucchini skin, as described in notes, above. (Save remaining zucchini for other uses.) Set aside.
2. In a 3- to 4-quart pan over high heat, bring broth, onion, celery, turnip, and potato to boiling. Reduce heat, cover, and simmer until potato is tender to bite, about 6 minutes. Add half the beans and their liquid; return to simmering, then cook, covered, for 5 to 10 minutes to blend flavors. Keep warm and set aside.
3. In a blender or food processor, whirl remaining beans and liquid, basil, and garlic until smooth. Set aside.
4. Cook pasta, uncovered, in 4 quarts boiling water and 1 tablespoon salt until almost tender to bite, about 5 minutes; after 3 minutes, add broccoli. Stir in julienned vegetables and boil until just tender to bite, about 1 minute. Drain, rinse with hot water, remove broccoli, and keep foods warm.
5. Stir basil mixture into broth mixture. Spoon into 4 wide, rimmed dinner plates. Mound pasta in the center. Scatter tomato and broccoli around plate rims. Offer pepper and lemon wedges.