Lay the vegetables out on a pan and lightly brush them with olive oil and season with salt and pepper. Place the mushrooms on the grill pan, smooth side down. Grill until juices collect in the cap and mushrooms soften, about 3 minutes. Turn them over and cook until slightly charred around the edges and the center is very tender, about 3 minutes more. Grill zucchini and yellow squash until lightly charred. Put the peppers on the grill pan skin side down and grill until juicy and charred, about 6 minutes. Turn down heat slightly and grill the onions, turning once or twice, until they are tender, about 20 minutes.