Ingredients
4 whole chicken legs, split, or 4 thighs and 4 drumsticks (2 1/2 pounds)
Kosher salt and freshly ground pepper
3 tablespoons vegetable oil
1 large white onion, quartered lengthwise and peeled (stem end intact)
1 quart low-sodium chicken broth
3 dried guajillo chiles, stems and seeds removed
1 dried ancho chile, stem and seeds removed
1 fresh jalapeño or serrano chile, stem removed (ribs and seeds removed for less heat, if desired)
3 cloves garlic, peeled
1 teaspoon dried oregano
1/3 cup packed fresh cilantro sprigs, plus more for serving
1/2 teaspoon cumin seeds
2 tablespoons fresh lime juice, plus wedges for serving
1 can (29-ounces) hominy, drained
Sliced radishes and shredded cabbage, for serving (optional)
Tostadas or tortilla chips, for serving (optional)
Preparation
Season chicken with salt and pepper. Heat 2 tablespoons oil in a pot over medium-high. Add chicken, skin-sides down, and cook, flipping once, until browned all over, 7 to 9 minutes (do not crowd pan; brown in batches if necessary). Add 2 onion wedges, broth, and 3 cups water.
Bring to a boil, then reduce heat to medium and cook at a bare simmer (small bubbles sporadically emerging at surface) until chicken is just cooked through, 20 to 25 minutes. Transfer chicken to a plate. Strain broth and return to pot.
Meanwhile, heat a heavy skillet (preferably cast iron) over medium-high. Add dried chiles and cook, turning a few times, until blistered in places and fragrant, 1 to 2 minutes. Transfer to a bowl and add enough hot tap water to cover; let stand 10 minutes.
Meanwhile, add remaining 1 tablespoon oil to skillet. Add 1 onion wedge, jalapeño, and garlic; cook, turning a few times, until golden brown in places and beginning to soften, 7 to 9 minutes.
Transfer mixture to a blender (do not wipe skillet clean), along with reconstituted dried chiles and 1/2 cup soaking liquid, oregano, cilantro, cumin, lime juice, and 1 teaspoon salt. Purée until smooth. Return mixture to skillet and simmer over medium heat, stirring occasionally, until reduced and darkened slightly, 8 to 10 minutes.
Remove and discard skin and bones from chicken; shred meat into bite-size pieces (leave drumsticks whole, if desired). Return chicken to pot with puréed-chile mixture and hominy. Simmer, stirring occasionally, 15 minutes. Season to taste. Chop remaining onion wedge and serve soup with onion, radishes, cabbage, tostadas, cilantro, and lime wedges.
