Grind a teaspoon of the green peppercorns and mix with the salt, clove, and cardamom. Rub the duck breasts with this mixture and marinate for about 30 minutes before cooking. Meanwhile, blanch the potatoes in abundant, salted boiling water until just tender. Drain and keep warm.
Score the duck breasts in a cross-hatch pattern and then place skin side down in a single layer and cook, without turning, over very low heat, until the fat has rendered out of the skin and the skin is crispy and golden, about 40 minutes.
When the skin is golden and the fat is rendered, strain and reserve the fat. Turn the pan up to high, flip the duck breast to skin side up, and cook briefly about 3 minutes. Remove the duck breast from the pan and allow to rest 10 minutes.
While the duck is resting, return the pan to the heat with one tablespoon of the reserved duck fat. Toast the garlic and the remaining green peppercorns in the duck fat and when the garlic begins to color and become fragrant, add the chicken stock and cook briskly until reduced by two-thirds.
Toss the warm potatoes with the coconut oil, the jalapeño, and the chopped cilantro. Season lightly with salt. Serve the duck breast sliced, with the potatoes and the green peppercorn sauce.