Season the chicken on both sides with salt and pepper. Coat well with the breadcrumbs using your hands to pack them on tight.
Heat a large sauté pan over medium heat. Once hot add the oil. Fry the chicken on both sides to golden brown to an internal temperature of 160 degrees using a thermometer. Then place on paper towels to drain excess grease and season with a pinch of salt.
Drain some of the grease out of the pan if needed so there are about 1 to 2 tablespoons left. Saute the onion until soft. Stir in the flour until fully incorporated. Stir in the broth and capers. Bring to a low simmer, adjust the heat accordingly so the broth thickens to a creamy consistency. Season with salt and pepper to taste. ** If desired: Stir in a little of the brining liquid from the caper jar to give a hint of briny flavoring.
Spoon the sauce over the chicken. Garnish with parsley. Serve with bread.
Notes
Pro tips: Butterfly the chicken: Lay the breasts down on a cutting board, using a sharp knife parallel to the cutting board slice the breasts evenly through the middle (carefully) all the way in half.