Cut all the vegetables in large pieces for the grill. Slice large eggplants about ½ inch thick and thin ones in half lengthwise. Slice the zucchini lengthwise a little thinner than the eggplant. Cut the bell peppers lengthwise in thirds and trim out the cores and seeds. Thickly slice the onions crosswise. Cut the tomatoes in half.
Whisk together all the marinade ingredients, or pulse them briefly in a blender.
Layer the vegetables in a large glass or ceramic dish, brushing them generously on both sides with the marinade as you put them in and leaving the tomatoes for last. Drizzle the remaining marinade over the vegetables in the dish and place the tomatoes cut side down on top of them. Leave the vegetables to marinate for at least an hour, longer if you have plenty of time.
Fire up the coals! When they are ready, grill the vegetables until they are charred and blistered just the way you like them, and tender enough to be flexible but not mushy. The exact time is impossible to call, as it varies with the heat of the coals and the distance between the grate and the coals, but probably 3 to 4 minutes on a side if the coals are nice and hot. I start with the peppers, and then amuse myself by pulling off their charred skins as I grill the eggplants, zucchini, and onions. Grill the tomatoes last, giving them a minute or 2 on the cut side, then turning them and leaving them on the coals, on their skins, until they are completely soft, up to 7 minutes.
Let the vegetables cool until you can handle them, then scoop the tomatoes out of their skins into a bowl and discard the skins. Drizzle the marinade left in the dish over the tomatoes and crush them with your hands, breaking them up. That’s the sauce.
Cut all the other vegetables into generous bite-sized strips and mix them with the tomatoes. Taste, and add more salt, pepper, and balsamic vinegar if needed to get the proper level of zinginess. Serve hot, with a pilaf or rice or orzo, and drizzle a little olive oil on top of each serving.