Slice top off of garlic, drizzle with olive oil, and sprinkle with sea salt. Wrap in foil and place on grill over indirect heat. Roast until garlic is soft and caramelized, 30 - 45 minutes.
Place eggplant on grill and roast with lid closed, turning occasionally, until eggplant is soft, 30 - 45 minutes.
Cut eggplant in half and place in colander to drain and cool. Set garlic aside to cool.
Peel and dice eggplant. Mash 4 cloves of roasted garlic. Combine eggplant, mashed garlic, peppers, 3 tablespoons olive oil, lemon juice, basil, salt, and pepper. Taste and adjust seasonings.
Garnish with an extra drizzle of olive and fresh basil.