Step 1

Pat duck legs dry with paper towels; season on both sides with salt. Place, skin side up, on a plate and chill, uncovered, at least 8 hours and up to 12 hours.

Step 2

Pick ¼ cup leaves with tender stems from cilantro bunch; set aside. Coarsely chop rest of bunch and place in a blender along with ⅓ cup water; blend until smooth. Measure out ½ cup cilantro purée and set aside; discard remaining purée. Rinse out and reserve blender.

Step 3

Place racks in middle and lower third of oven; preheat to 325°. Prick sweet potato all over with a fork and wrap in foil; place on a small rimmed baking sheet. Bake on lower rack until fork-tender, 1–1½ hours. Remove sweet potato from oven; set aside.

Step 4

Meanwhile, place duck legs, skin side down, in a cold, dry large Dutch oven or other heavy ovenproof pot. Set over medium heat and cook until skin is browned and a good amount of fat has cooked out, 8–10 minutes. Turn duck over and cook until browned on the other side, about 5 minutes. Transfer duck, skin side up, to a plate, leaving fat in pot (you should have about ¼ cup; add vegetable oil if short).

Step 5

Add onion to pot and season lightly with salt. Cook (still over medium heat), stirring occasionally, until softened and starting to brown, 10–12 minutes. Add garlic and cook, stirring often, until fragrant, about 1 minute. Add ají amarillo paste; cook, stirring occasionally, until jammy, 5–7 minutes. Stir in pepper, cumin, and reserved cilantro purée. Cook, stirring often, until darkened, thick, and most of moisture has cooked off, 5–7 minutes.

Step 6

Add pilsner, scraping up any browned bits from bottom of pot with a wooden spoon. Cook, stirring occasionally, until thickened, 5–7 minutes. Stir in broth and bring to a boil. Using tongs, place duck, skin side up, in pot.

Step 7

Transfer pot to middle rack in oven and bake, uncovered, 30 minutes. Partially cover pot and continue to bake until sauce is slightly thickened, 20–30 minutes longer. Uncover pot and stir in potato and carrot. Cover pot; continue to bake until duck and vegetables are tender, 20–25 minutes more. Stir in peas.

Step 8

Unwrap reserved sweet potato and place in blender. Add cream, butter, and a pinch of salt. Blend, adding water as needed (up to 3 Tbsp.), until you have a thick but pourable purée. Taste and season with more salt if needed.

Step 9

Divide duck legs and sauce between bowls. Swirl sweet potato purée into sauce; top with reserved cilantro.