Combine the balsamic vinegar, honey, currants and cayenne in a small pot. Bring to a boil, reduce to a simmer and reduce by half to form a thick, syrupy glaze. Remove from the heat and set aside.
With the point of a knife, score the skin side of the duck breasts in a crosshatch pattern, being careful not to pierce the flesh.
Season the duck breasts with the salt and pepper. Heat a saute pan over medium heat 2 minutes before adding the breasts, skin-side down. Cook over medium to low heat approximately 6 to 8 minutes to render the fat.
Carefully remove the excess fat from the saute pan, then turn the breasts over and saute the flesh side 3 to 4 minutes before removing the duck breasts from the pan.
The breasts should now be medium rare. Slice lengthwise or crosswise and arrange several slices on each plate. Reheat the balsamic vinegar glaze and drizzle some over each of the duck breasts. Sprinkle with toasted pine nuts and serve with Ginger Chestnut Stuffing