Step 1Heat the oven to 400 degrees. In a small roasting pan, combine the mushrooms, eggplant and onion. Drizzle the olive oil over and season with a pinch each salt and pepper, or to taste, gently stirring to combine. Roast until tender, 30 to 35 minutes, stirring every 10 to 15 minutes. Remove and cool slightly, then taste and adjust the seasoning if desired.
Step 2Bring about 1 1/2 quarts water to a boil in a medium saucepan and add a pinch of salt. Add the radish slices, cover and cook 4 minutes. Add the carrot slices and continue to cook until the radish and carrot are crisp-tender, 3 to 6 minutes more. Remove with a slotted spoon.
Step 3Return the liquid to a boil. Add the broccoli florets and return to a boil. Boil uncovered over high heat until they are crisp-tender, 3 to 5 minutes; remove with a slotted spoon. Add the asparagus stem pieces and cook until crisp-tender, 1 to 2 minutes. Add the asparagus tips and cook until the asparagus is crisp-tender, 1 to 2 minutes; remove with a slotted spoon. (Save the broth if you'd like; it is good for soups.)
Step 4On a platter, arrange mounds of the roasted and cooked vegetables; spoon the chickpeas into a serving bowl. Sprinkle toasted sesame seeds over the roasted vegetables, carrots and radishes. Serve the green tahini sauce in a small bowl in the center of the platter. Serve the vegetables hot, warm or at room temperature and the sauce at room temperature.