Set the oven at 400℉. Sprinkle the salt over the eggplant and let sit for 15 minutes, then wipe off any accumulated water. Mix together olive oil and paprika and then brush each side of the sliced eggplant with oil mixture and place on a lined sheet tray. Roast for 15–20 minutes or until the eggplant is very soft.

Divide the eggplant between the slices of bread, then top each one with cheese. Place beneath the broiled and cook until the cheese is melted. Divide arugula between the sandwiches then cut in half and serve.