How to Make It
Lightly season the duck breasts all over with salt and set them skin side down on a large baking sheet. Refrigerate uncovered until the meat looks shiny, about 30 minutes.
Meanwhile, in a medium skillet, melt the butter. Add the shallot and cook over moderate heat, stirring, until just starting to brown, 4 minutes. Add the dried sour cherries and sugar and cook, stirring occasionally, until the sugar is dissolved and just starting to caramelize, 5 minutes. Add the vinegar and 1/4 cup of water and cook, stirring, until the liquid is absorbed, 3 minutes. Fold in the parsley and thyme and season the stuffing with salt and pepper. Let cool completely.
Preheat the oven to 400°. Set the duck skin side down on a work surface. Spread the cherry stuffing over the breasts evenly. Fold over one side of each breast to enclose the stuffing and tie them in 5 places with kitchen twine to make 4 neat roasts.
Heat a large ovenproof skillet. Season the roasts all over with pepper and cook over moderate heat, turning occasionally, until the skin is browned and nearly crisp, 10 to 12 minutes; spoon off the excess fat in the skillet as needed.
Transfer the skillet to the oven and roast the duck for about 12 minutes, until an instant-read thermometer inserted in the thickest part of each breast registers 118° to 120°. Transfer the duck breasts to a carving board and let rest for 5 minutes. Snip off the kitchen twine. Thinly slice the roasts crosswise and serve.