Step 1Take the duck breasts out of the refrigerator about 30 minutes before cooking and allow to come to room temperature. Remove any silver skin from the meat. Rinse and pat dry. Using a sharp knife, score the skin in a crisscross pattern without cutting into the meat. Sprinkle the skin with salt and pepper. Cover with plastic wrap until ready to cook.
Step 2Melt the butter in a large nonstick skillet. Add the duck breasts, skin side up, and sear over medium-high heat, about 2 minutes. Add 2 tablespoons stock to deglaze the pan, letting the liquid boil for about 1 minute.
Step 3Turn the duck breasts skin side down. Season the meat side with salt and pepper. Reduce the heat to low and cook for 15 minutes without turning the breasts. As it cooks, the skin will crisp and render fat. Turn the breasts over again and cook the meat side until done (it will feel springy to the touch), about 2 to 3 minutes for medium rare.
Step 4Remove the breasts from the pan, placing them on a warm platter. Cover loosely with foil.
Step 5Carefully pour out the rendered fat into a small metal bowl.
Step 6Place 2 teaspoons of the fat into the same skillet. Over medium heat, add the shallots and saute until fragrant, 30 seconds to 1 minute.
Step 7Add the cherries, and raise the heat to high. Pan-roast the cherries, shaking to cook evenly, about 2 to 3 minutes (do not let the skins pop). Remove from heat. Add to the pan the remaining 2 to 3 tablespoons stock, plus the juices that the duck breasts have released.
Step 8Slice the duck breasts into one-third-inch-thick slices, cutting at a diagonal starting at the narrower end. Transfer to a warm platter, slightly fanning the slices. Sprinkle with freshly ground black pepper and spoon the cherries over.