Soak the wood chips in water for at least 30 minutes.
Fill a medium saucepan with salted water and bring to a boil on the stove. Rinse the farro in a fine-mesh sieve under cold water, add it to the saucepan, and boil until fully cooked but still al dente, according to package directions. Drain in a fine-mesh sieve, rinse under cold running water, and let cool.
In a small bowl combine 1½ teaspoons salt, ½ teaspoon pepper, the ginger, paprika, and cardamom. Slip your fingers beneath the skin (with the fat) on each breast half to loosen it from the meat, but keeping it attached at the center. Using kitchen scissors, trim away some of the skin, leaving a strip about 4 centimeters wide that runs the entire length of each breast half. Make four to five diagonal slashes in the skin on each breast half, slashing down to but not through the meat. This trimming and slashing procedure will help prevent flare-ups and allow the fat to melt and the skin to crisp during grilling. Lightly brush the breast halves with oil and season evenly with the spices.
Prepare the grill for direct cooking over medium heat (180° to 230°C). If you're using a charcoal grill, keep a small part of the charcoal grate clear of briquettes as a safety zone of indirect heat.
Prepare the grill for cooking over medium heat (200°C). If you're using a charcoal grill, keep a small part of the charcoal grate clear of briquettes as a safety zone of indirect heat.
Brush the cooking grates clean. Drain and add the wood chips to the charcoal or to the smoker box of a gas grill, following manufacturer’s instructions, and close the lid. When the wood begins to smoke, cook the duck, skin side down first, over direct medium heat, with the lid closed, until the skin is browned and the meat is cooked to your desired doneness, 8 to 10 minutes for medium rare, turning once (if flare-ups occur, move the duck temporarily over indirect heat). Remove from the grill and let the duck rest while you finish the salad.
Brush the cooking grates clean. Drain and add the wood chips to the charcoal or to the smoker box of a gas grill, following manufacturer’s instructions, and close the lid. When the wood begins to smoke, cook the duck, skin side down first, over medium heat, with the lid closed, until the skin is browned and the meat is cooked to your desired doneness, 8 to 10 minutes for medium rare, turning once (if flare-ups occur, move the duck temporarily over indirect heat). Remove from the grill and let the duck rest while you finish the salad.
In a large skillet over medium-high heat on the stove, warm 2 tablespoons oil. Add the scallions, red pepper, and red pepper flakes and sauté until the vegetables are softened, 2 to 3 minutes. Add the farro and the vinegar. Season with salt and pepper. Sauté for 1 to 2 minutes more. Remove the skillet from the heat.
Cut the duck across the grain into thick slices and serve warm with the farro and vegetable salad.
Note: If you wish, substitute two large Moulard duck breast halves (magrets) for the four Pekin breast halves. Each magret will weight about 455 grams. Cut each in half on a slight diagonal to make two pieces.
