Remove skin from duck leg and cut skin into 1/4-inch pieces. Cook skin in a 1- to 1 1/2-quart heavy saucepan over low heat, stirring occasionally, until fat is rendered and skin is golden brown, 8 to 12 minutes. Transfer duck skin with a slotted spoon to paper towels to drain and season with salt. Pour off and discard fat from saucepan (or reserve for another use), then wipe pan clean and set aside.
While skin cooks, remove duck meat from bones, reserving bones, and finely shred.
Toast chile in dry saucepan over moderate heat, turning with tongs, until fragrant and pliable, about 2 minutes, then transfer to a bowl. Cover chile with boiling-hot water and soak until softened, about 20 minutes. Drain chile and transfer to a blender.
While chile soaks, add onion and garlic to dry saucepan and cook over moderate heat, stirring occasionally, until browned, 2 to 3 minutes. Add water, oregano, honey, cumin, and reserved bones and simmer, uncovered, 20 minutes. Discard bones.
Blend broth mixture with softened chile and 1/4 teaspoon salt in blender until very smooth (use caution when blending hot liquids). Transfer purée to saucepan. Add hominy and shredded duck meat and simmer, covered, 10 minutes. Stir in cilantro and salt to taste, then serve topped with duck skin.
*Available at butcher shops, some supermarkets, and D'Artagnan (800-327-8246).
**Available at Latino markets, many supermarkets, and Chile Today-Hot Tamale (800-468-7377).