A less spicy riff on a Mexican posole, we skip the traditional pork in favor of chicken. Be generous with the black pepper for a little zip.
Heat oil in a large pot over medium-high heat. Sear chicken thighs for about 4 minutes per side. Remove chicken and set aside. Reserve 1 tablespoon oil and discard remainder.
Sauté onions for 2 minutes, then stir in tomato paste, oregano, cilantro, garlic, and a pinch of salt. Add cabbage, seared chicken, and stock, then cover and bring to a boil. Reduce heat to maintain a simmer for about 45 minutes.
Remove chicken and pull meat from bones, discarding bones and skin. Add hominy to pot, stir, and increase heat to medium. Meanwhile, use two forks to shred chicken, then return meat to pot. To serve, garnish with sliced radishes, a squeeze of lime, and cilantro leaves.