Reserve 4 quince quarters and 3/4 cup poaching liquid from Poached Quinces. Reserve remaining quince quarters and liquid for another use. Cut 4 quince quarters into cubes; set aside.
Combine 1/2 cup reserved poaching liquid, five-spice powder, ginger, and garlic in a large zip-top plastic bag. Add duck to bag; seal and toss to coat. Marinate in refrigerator at least 24 hours or up to 2 days, turning bag occasionally.
Preheat oven to 400°.
Remove duck from marinade; discard marinade. Sprinkle duck evenly with salt and pepper. Heat a large ovenproof skillet over medium-high heat. Place duck, skin side down, in pan; cook 1 1/2 minutes or until skin is golden brown. Turn meat over; cook 1 minute. Place pan in oven. Bake at 400° for 15 minutes or until a thermometer registers 160° (medium) or until desired degree of doneness. Remove duck from pan, reserving 2 teaspoons drippings in pan. Place duck, skin side down, on a cutting board or work surface. Brush meaty side of duck with remaining 1/4 cup poaching liquid.
Heat reserved drippings in pan over medium-high heat. Add cubed quince quarters; sauté 5 minutes or until golden brown. Remove from heat; stir in sliced green onions.
Remove skin from duck; discard. Cut duck diagonally across grain into thin slices. Divide duck slices evenly among each of 4 plates; top each serving with 1/4 cup quince mixture. Serve immediately.
Wine note: These duck breasts have it all--sweetness from the Poached Quinces, richness from the duck, and spiciness from the five-spice powder. Is there one wine that can act as a perfect counterpoint? Yes: pinot noir. A top pinot will have the acidity to balance the richness of the duck while possessing grace notes of ripe fruit and spiciness to mirror the quince and five-spice powder. A terrific choice: Alderbrook Pinot Noir 2002 from California's Russian River Valley ($24). -Karen MacNeil