Turn the eggplant so that the flesh side faces up, and lightly score the flesh with a pairing knife to create a diamond pattern. Season the flesh side lightly with salt and let stand for 5 to 10 minutes. < this will help to draw some of the excess moisture out of the eggplant before cooking.
Pat the eggplant dry and brush the flesh of the eggplant with a generous amount of olive oil, about 2 tablespoons. Season again light with salt and pepper.
Place the eggplant on a hot grill flesh side down. Cook 3 minutes or until the edges begin to char and turn black. Flip the eggplant and cook 3 minutes more on the skin side. Turn again for a finish cooking 1 minute on the flesh side. Remove the eggplant to the rack with the steaks and immediately spread the flesh side with espresso butter. Let stand 1 minute.