In a large Dutch oven or stockpot, add the hominy, chicken breast, onion, garlic, water, bouillon, salt, pepper and oregano. Cook on medium high covered.
Meanwhile make the salsa verde: In a small skillet, add the olive oil and saute the onion, the chiles and garlic over medium high heat. Saute for 2 minutes.
To a blender or food processor, add the sautéed vegetables, tomatillos, poblano peppers, cilantro, bouillon, salt and pepper. Blend until smooth.
Add about 2 cups of the salsa verde to the chicken and hominy mixture. When the chicken is cooked, shred with 2 forks, then transfer back to the pot.
Taste and season with salt and pepper, if needed.
To serve top with avocado, cilantro, a squeeze of lime juice and shredded cabbage. Tortilla chips or tostadas make a great pairing.