For each sandwich, cook one large egg over medium heat in spray-coated nonstick pan until whites are set and yolks begin to thicken, but are not hard. Flip over and cook briefly on other side for additional firmness.
Split muffaletta bread and cover bottom half with 2 tablespoons olive tapenade, then top with one slice provolone, 2 slices capicola, 1 slice salami, a fried egg and one slice of ham. Dress the top half of the bread with 2 tablespoons caper cream cheese and press it down on top of the sandwich. Serve immediately.
NOTE: Do not allow raw or cooked eggs to remain at room temperature for longer than one hour (including preparation and service time).