Preheat oven to 425║.
Cut eggplant into 3/4 inch chunks.
Place in a bowl and toss with 4 tablespoons oil, salt and pepper to taste.
Transfer to a heavy baking sheet.
Roast until just tender and lightly browned, about 30 minutes, stirring once or twice with a spatula to make sure the chunks aren't sticking to the sheet.
Transfer to a large, shallow bowl.
Meanwhile, with a small knife, cut around the head of garlic at the "equator" penetrating the paper skin but not the cloves.
Remove the papery outer layers from the top half of the head (opposite the roots), exposing the cloves.
Place garlic on a large square of foil and drizzle with 1 tablespoon olive oil.
Loosely wrap the foil around it, sealing edges tightly.
Slip the garlic into oven alongside eggplant and bake until cloves are soft, about 45 minutes.
Remove seeds and ribs from bell peppers.
Cut peppers into 1 inch pieces.
In a large skillet, heat remaining 1 tablespoon olive oil over high heat. Add peppers and onion.
Season with salt and pepper and sautÚ until tender, but not mushy, about 8 minutes.
Transfer to bowl with eggplant.
Add cherry tomatoes to the skillet adding salt and pepper if needed.
Saute just to heat through, about 1 minute. Transfer to bowl with eggplant.
Add parsley. Squeeze the garlic out of the skins in a small bowl and mash to a puree.
Whisk in vinegars. Add gently add a little bit at a time to the eggplant mixture.
Taste and add more vinegar if needed.