Cook the Chicken: In a large pot, combine chicken, chicken broth, onion, garlic, bay leaves, and salt. Bring to a boil, reduce to simmer, and cook until chicken is tender (about 25–30 minutes). Remove chicken, shred it, and set aside. Strain and reserve the broth.
Make the Green Sauce: Roast tomatillos, poblanos, and jalapeños under a broiler or on a hot skillet until charred and blistered. Peel skins from poblanos and jalapeños. Blend roasted vegetables with cilantro, cumin, and a splash of reserved broth until smooth.
Build the Pozole: In the same pot, heat oil over medium heat. Add the green sauce and cook for 5 minutes until fragrant. Pour in reserved chicken broth, add hominy and oregano, and simmer for 15 minutes. Stir in shredded chicken.
Finish u0026 Serve: Taste and adjust seasoning with salt and pepper. Ladle pozole into bowls, and serve with your choice of garnishes.