Duck Confit Sliders, Banh-Mi Style

Duck Confit Rendered duck fat from 1 duck, at warm temperature, plus more fat ( chicken, duck, bacon, oil, etc.) as needed 4 duck legs and thighs Salt Pinch sugar 2 teaspoons whole coriander 1 teaspoon sweet smoked paprika 1 teaspoon ground cinnamon 2 teaspoons peppercorns Quick Carrot Pickle 1/4 cup sugar 1 shallot, peeled and trimmed 1 clove garlic, peeled and trimmed 1 jalapeno 1 bay leaf 2 tablespoons salt 1 teaspoon coriander seeds 1 teaspoon peppercorns 1 cup white wine vinegar 1 cup water 2 carrots, peeled and julienned Aioli 2 egg yolks 1 clove garlic, minced Zest and juice of 2 limes 1/3 to 1/2 cup liquid duck fat Hot sauce, to taste Salt Assembling 4 to 6 slider rolls 1 cup freshly picked cilantro leaves