In a 2-quart sauce pot, combine cider, chicken stock, cinnamon stick, cloves, peppercorns, and shallots. Bring to a boil over medium-high heat, then reduce heat so liquid just simmers. Continue to cook until mixture has reduced to 1 cup, 35 to 40 minutes. (Have a liquid measure nearby so you can check the volume as necessary.) Set sauce aside to cool a few minutes, then strain through a fine mesh sieve. Reserve sauce. Discard solids.
Preheat oven to 425 degrees.
Season chicken breasts on both sides with salt and pepper. Heat olive oil in a 12-inch skillet over medium heat. Add breasts, skin-side down, and cook for 3 minutes. Reduce heat to medium-low, flip chicken, and cook 4 minutes longer. Transfer chicken breasts to oven and cook for another 10 to 12 minutes, or until internal temperature reaches 165 degrees on an instant-read thermometer. Remove chicken from oven and transfer to a serving platter.
Drain any remaining fat from hot pan, then return pan to stove over medium-high heat. Add sauce to pan and reduce by half, about 4 minutes, or until syrupy. Remove from heat.
Either serve whole or slice breast diagonally into 1/4-inch slices. Serve with sauce spooned over the top.
Cook's Note: "Frenched" refers to a technique where the meat is cut away from the end of a rib or bone, in this case the wing bone, leaving a portion of the bone exposed. If you are uncomfortable doing this yourself, ask your butcher to do it for you.