Duck is surprisingly simple to cook, and it always rewards with luscious, rich flavor—making it perfect for a special dinner. Here, you’ll be using the meat two ways: first, breasts are seared in the pan until the skin is rendered and crisp, and then the potatoes are tossed in the drippings to give them a marvelous, lingering flavor.
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Wash and dry all produce. Halve potatoes lengthwise. Place in a medium pot with enough salted water to cover by 2 inches. Bring to a boil and cook until easily pierced with a fork, 12-15 minutes. Drain well, then return potatoes to pot. Meanwhile, trim and discard woody ends from asparagus. Mince chives.
Pat duck dry with paper towels; season generously with salt and pepper. Place skin sides down in a large pan. Cook over medium heat until skin is crisp and most of the fat has rendered, 15-20 minutes, pouring off and reserving fat as it renders. (TIP: Lower heat if skin begins to brown too quickly.) Flip duck and cook to desired doneness, about 5 minutes more. Transfer to a cutting board and let rest.
Add just enough reserved duck fat to pot with potatoes to cover bottom surface. Heat pot over medium-high heat and cook, stirring, until potatoes are browned and crisp, 3-5 minutes. Remove from pot and season with salt and pepper.
Meanwhile, add asparagus and 2 tsp water (4 tsp for 4 servings) to pan used for duck over medium heat. Cover and steam until bright green, 2-4 minutes. Uncover, then increase heat to mediumhigh and add a drizzle of duck fat and tomatoes. Cook, stirring occasionally, until asparagus is tender and tomatoes burst, 3-5 minutes. Season with salt and pepper. Transfer to a plate and set aside.
Stir demi-glace, ¼ cup water (⅓ cup for 4 servings), and 2 TBSP butter (4 TBSP for 4) into same pan. Bring to a boil, then remove from heat. Season with salt and pepper.
Slice duck crosswise. Divide between plates along with potatoes and veggies. Spoon sauce over everything. Sprinkle with chives.