Cut two to four 1/4 -inch-thick slices from one of the apples (1 slice for each serving) to roast. Peel and chop the remaining apples. Set aside.

Preheat oven to 400 degrees F. Place the duck breasts, skin sides up, on a cutting board and score all over in a tiny crosshatch pattern so that the fat will render (melt out) and the skin will crisp. Season all over with salt and pepper. Lightly coat the bottom of a large saute pan with a 2-count of oil (about 2 tablespoons) and place the pan over medium heat. When the oil is very hot, add the breasts, skin sides down, and cook about 8 minutes, basting with rendered fat, until the skin is brown and crispy. Place the duck breasts, skin sides up, and the apple slices on a roasting tray. Roast for 5 to 7 minutes for medium-rare (130 to 135 degrees F in the thickest part of breast).

Meanwhile, in a large saucepan combine chopped apple, onion, thyme, and butter and place over medium heat. Add apple juice; cover and simmer for 12 to 15 minutes, until apples are soft. Puree in a food processor and season with salt and pepper.

Slice duck breast; serve over apple-onion puree with roasted apple slices. If you like, garnish with micro sprouts.