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 1/8 teaspoon each salt and black pepper. Add 1/2 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 1/8 teaspoon each salt and black pepper. Add 1/2 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.
You can substitute red bell pepper for the yellow bell pepper and mayonnaise for butter.
To keep sodium in check, look for Halloumi with 350 mg sodium or less per ounce. In place of the Halloumi, try tofu. Use 8 slices extra-firm tofu (not silken). Pat dry with paper towels. Season tofu with 1/8 teaspoon each salt and black pepper. Cook tofu in a skillet for 3 minutes per side.