Prepare a grill for indirect heat. If using a charcoal grill, build the hot coals on one side only. If using a gas grill, heat one side only to medium-high heat.
Place the eggplant over the hot (direct heat) side of the grill and cook until charred and softened, turning it as it cooks, about 20 minutes. Move the eggplant to the cool (indirect heat) side of the grill and close the grill if the outside chars before the eggplant softens.
Remove the eggplant from the grill and place it in a resealable plastic bag to steam, about 10 minutes. Peel the eggplant, use a spoon to remove and discard the seeds, then chop the eggplant and place it in a large bowl. Fold in the feta, parsley, lemon juice and garlic. Season with salt and pepper. Set aside.
Meanwhile, drizzle the tomatoes with oil and season with salt and pepper. Pick the tomatoes up by the vine and place them on the hot (direct heat) side of the grill. Cook until blistered and beginning to crack open, 2 to 3 minutes. Remove from the grill and set aside while you cook the fish.
Season the fish on both sides with salt and pepper then drizzle with oil. Place on the hot (direct heat) side of the grill and cook until nicely charred and cooked almost all the way through, 2 to 3 minutes per side.
To serve, spoon some of the eggplant onto a plate or platter. Place the fish on top along with some of the tomatoes and drizzle with olive oil.