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.
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