One day before serving, make the caponata: Preheat a grill to medium high. Pierce the eggplant all over with a fork. Grill, turning often, until charred all over and softened, 25 to 30 minutes. Meanwhile, coat the bell pepper with 1 teaspoon olive oil. Grill, turning as needed, until charred all over, about 15 minutes. Transfer the vegetables to separate bowls; cover the pepper and let cool.
Peel the charred skin from the pepper (do not rinse). Cut in half, discard the seeds and finely dice. Remove the skin from the eggplant. Cut in half lengthwise and scoop out the seeds. Return the pulp to the bowl and set aside until juicy, about 15 minutes. Transfer the eggplant to a cutting board and finely chop; reserve the juices that have collected in the bowl.
In a medium heavy saucepan, heat the remaining 3 tablespoons plus 2 teaspoons olive oil over medium-high heat. Add the onion and celery, season with salt and pepper and saute until the onion begins to soften, about 5 minutes. Add the garlic and saute until fragrant, about 1 minute. Add the diced bell pepper, tomato and sugar and saute until the tomato softens, about 3 minutes. Add the olives, capers, raisins and the eggplant and eggplant juices and cook 3 minutes. Stir in the vinegar and chocolate.
Reduce the heat to low and cook gently, stirring occasionally, for 15 minutes to allow the flavors to blend. Transfer to a bowl and let cool. Cover and refrigerate overnight.
Preheat a grill to medium high and prepare for indirect grilling: For a charcoal grill, bank the hot coals to one side and leave the other half empty. For a gas grill, preheat all the burners, then turn off half the burners and keep the others on medium-high heat.
Grill the steak: Pat the meat dry with paper towels. Lightly brush with olive oil and season with salt and pepper. Place the steaks on indirect heat (the unlit side of the grill); cover and cook, turning halfway through, until an instant-read thermometer inserted into the center registers 110 degrees F, about 30 minutes. Transfer to direct heat and cook, turning, until the steaks are charred and the thermometer registers 125 degrees F to 130 degrees F for medium-rare doneness, 4 to 6 more minutes. Transfer to a cutting board and let rest 10 minutes.
Stir the parsley and basil into the caponata; season with salt and pepper. Carve the meat from the bones and slice against the grain. Serve with any collected juices and the caponata.