With a sharp knife, score the duck skin in a diamond pattern, being careful not to cut all the way through to the meat. Season the duck all over with salt and pepper. Put the duck skin side down in a cold 12-inch skillet. Cook over medium heat without moving, spooning off the excess fat occasionally, until the skin becomes light golden-brown, 8 to 9 minutes.
Loosen the duck from the pan with a spatula. Raise the heat to medium high and continue cooking, skin side down, until the skin is thin, crisp, and browned, about 4 minutes. Turn the duck and continue cooking until an instant-read thermometer registers 135°F in the thickest part of a breast for medium rare, about 10 minutes more. Transfer the duck to a plate.
Pour off all but 1 Tbs. of the fat from the skillet. Add the grapes and cook over medium-high heat, stirring often, until lightly browned but still firm, about 3 minutes. With a slotted spoon, transfer the grapes to the plate with the duck. Add the shallot to the skillet and cook until slightly softened, about 1 minute. Add the wine and cook, stirring up the browned bits, until all the liquid evaporates, 2 to 4 minutes. Add the chicken broth and saba and boil until the mixture reduces to 2/3 cup, 5 to 6 minutes. Season to taste with salt and pepper. Add the grapes, duck, and any juices from the plate to the skillet. Simmer gently for about 1 minute, turning the duck to coat it with the sauce. Thinly slice the duck and divide it among 4 plates. Spoon the sauce and grapes over the duck. Sprinkle with the parsley and serve immediately.