Heat 1 tablespoon oil in a large skillet over medium heat. Add bell pepper and onion; cook until very tender, about 8 minutes. Transfer to a separate skillet. Stir in harissa sauce.
Brush both sides of eggplant slices with remaining 2 tablespoons oil. Sprinkle with ⅛ teaspoon each salt and black pepper. Add ½ of the eggplant slices to the skillet. Cook until browned and tender, about 3 minutes per side. Repeat with remaining slices; keep warm.
Sprinkle Halloumi with remaining ⅛ teaspoon each salt and black pepper. Add ½ of the Halloumi to the skillet and cook for 2 minutes per side. Repeat with remaining slices.
Layer eggplant slices, bell pepper mixture, and Halloumi on 4 bread slices. Top with remaining bread slices. Spread outsides of sandwiches with butter.
Transfer 2 sandwiches to the large skillet; cover sandwiches with a plate weighted with cans of food. Cook until heated through and toasted, about 2 minutes per side. Repeat with remaining sandwiches.
