Step 1Heat the oven to 300 degrees. Cut the rhubarb stalks into 3-inch by half-inch sticks.
Step 2Combine the sugar, ginger, orange zest and a grind or two of pepper in a large mixing bowl. Add the rhubarb and toss to coat well. Set aside to macerate for 30 minutes.
Step 3Toss the rhubarb again to coat with the liquid that has collected. Arrange the rhubarb in a baking dish in as close to a single layer as possible, and use a spatula to scrape any remaining liquid or zest over it.
Step 4Cover tightly with aluminum foil and bake until the rhubarb is tender, 25 to 30 minutes. Don't stir or the rhubarb may fall apart.
Step 5While the rhubarb bakes, cut a shallow cross-hatching on the skin side of the duck breasts, through the skin but not through the fat to the meat. Season the breasts liberally on both sides with salt and pepper and the ground cloves and place on a plate. Cover tightly with plastic wrap and refrigerate. (This recipe may be prepared to this point up to 24 hours in advance; bring the duck to room temperature and gently warm the rhubarb before proceeding.)
Step 6When ready to cook, heat the oil in a large, heavy-bottom skillet over medium-high heat until it is hot. Pat dry the skin side of the duck breasts with a paper towel and place the breasts skin-side down in the hot pan. Sear until the skin side is a deep golden brown, 3 1/2 to 4 minutes. Reduce the heat to medium and turn the breasts over. Cook on the second side until they are medium-rare in the center, 3 to 5 minutes more.
Step 7Remove the duck breasts to a carving board and cut on a bias into thick, crosswise slices and arrange on a plate. Using a slotted spoon, gently lift the warm rhubarb sticks from the syrup and arrange beside the duck. Serve immediately.