• Peel and coarsely chop enough onion to measure ¾ cup [1½ cups]. Finely chop enough of the remaining onion to measure ¼ cup [½ cup]; set aside for garnish.
• Finely chop, press, or grate enough garlic to measure 2 teaspoons [4 tsp].
• If using the jalapeño, remove the stem, ribs, and seeds; coarsely chop the jalapeño. Wash your hands after handling.
• Rinse the hominy.

Prep and cook instructions are identical for both chicken options.

• Pat the chicken dry with a paper towel. Cut the chicken crosswise into 1-inch-wide strips, then cut the strips crosswise into 1-inch cubes. Season generously with salt and pepper.

In a large frying pan over medium-high heat, warm 1 to 2 tablespoons oil until hot but not smoking. Working in batches if needed, add the chicken and cook, stirring occasionally, until browned but not yet cooked through, 2 to 3 minutes. Transfer to a plate. Add more oil between batches if needed. Do not clean the pan.

In the same pan used for the chicken, if dry, add 2 to 3 teaspoons oil. Warm over medium-high heat until hot but not smoking. Add the coarsely chopped onion, season with salt and pepper, and cook, stirring occasionally, until starting to soften, 2 to 3 minutes. Stir in the garlic and cook until fragrant, about 1 minute. Add as much jalapeño as you like and cook, stirring occasionally, until starting to soften, 3 to 4 minutes.
Add the hominy, tomatillos, green chiles, oregano, chicken and any accumulated juices, and 1 cup [2 cups] water. Bring to a boil, reduce to a simmer, and cook, stirring occasionally, until the chicken is cooked through and the sauce has thickened slightly, 8 to 10 minutes. Season to taste with salt and pepper.
When the pozole is almost done, prepare the garnishes.

• Cut the lime into wedges.
• Strip the cilantro leaves from the stems.

Transfer the pozole to individual bowls and garnish with the cilantro, pumpkin seeds, and finely chopped onion. Serve with the lime wedges.