Escalivada (or Escalibada) is from the Spanish word escalivar (to cook in ashes), which is how this Spanish recipe is traditionally prepared.
Preheat the broiler. Flatten the red peppers slightly so that they lie flat and place them on a large, well-oiled broiler pan. Arrange the tomatoes, cut side up, and onion on the same pan and brush all vegetables with olive oil.
Broil the vegetables until they are soft and charred, about 15 minutes for the onion, a few minutes longer for the tomatoes and red peppers, transferring the vegetables to a platter as they finish cooking.
When all the vegetables are done, place the peppers in a bowl, cover it with plastic wrap, and let steam for 15 minutes.
While the vegetables are broiling, place a small flameproof rack, such as the rack from a toaster oven, directly over a gas burner and set the heat to medium. Place the eggplants on the rack over the flame and cook until soft and charred all over, 7 to 8 minutes, turning often so they all cook evenly.
Using tongs, transfer the eggplants to a plate and let cool enough to handle.
Peel the red peppers and tear them into strips. Peel the eggplants, remove and discard the stems, and tear the flesh into long strips.
Decoratively arrange the eggplants, peppers, tomatoes, and onion wedges on a platter, alternating the various vegetables.
Place the 3 tbsp olive oil, the garlic, and vinegar in a small bowl and whisk to mix.
Pour the dressing over the vegetables, sprinkle with salt and parsley, and let stand for about 1 hour before serving.
Serves 4 to 6