Which Came First? Chicken and Egg Sammies Deluxe

Season the chicken breast cutlets evenly with smoked paprika, salt and pepper. Heat 2 tablespoons extra-virgin olive oil in a large nonstick skillet over medium-high heat. Add chicken to pan and cook 2 to 3 minutes on each side. Remove from skillet and let rest, tented with foil. Wipe pan and add 2 tablespoons more extra-virgin olive oil. Beat eggs with salt, pepper, milk or half-and-half. Add roasted peppers to skillet and cook 30 seconds then add eggs and scramble to desired doneness with wooden spoon or spatula . Preheat broiler. While eggs cook, toast rolls under broiler, 1 minute, then remove from oven. To assemble, slice chicken and pile on bun bottoms. Top each sammy with 1/4 of the eggs and a slice of cheese . Place sammies back under broiler 30 seconds to melt cheese. Reserve the tops. When cheese has melted, transfer the sammies to plates and top with a pile of watercress then set bun tops in place.