Sear chicken: Lightly drizzle chicken thighs with some olive oil, then season with ½ teaspoon salt and ½ teaspoon pepper. Heat 1 1/2 tablespoons olive oil over medium-high heat in a large Dutch oven/soup pot. Sear the chicken until golden, about 2 minutes per side. Remove chicken to a plate but leave the drippings; set aside.
Make salsa verde: To a high-powered blender, add half of the salsa verde ingredients: the tomatillos, poblano peppers, onion, jalapeños, garlic, cilantro and 1/2 cup chicken broth. Pulse until coarsely chopped, scraping down the sides as needed then puree until smooth. Transfer to the soup pot. Repeat with remaining salsa verde ingredients. Simmer salsa verde: Add the oregano, cumin and chicken bouillon to the salsa verde. Simmer over medium heat, while scraping up the golden bits on the bottom of the pan, then stirring occasionally, until the sauce turns a deep green, about 12-15 minutes. Simmer soup: Add the chicken back to the pot along with the hominy and remaining chicken broth. Cover the soup to bring to a simmer, then displace the lid so it’s partially covering the pot, with about a one-inch opening. Simmer the soup for 12-15 minutes or until chicken is tender enough to shred.
Shred chicken: Once chicken is tender, remove it to a cutting board and shred with two forks. Meanwhile, continue to simmer the soup for an additional 5-10 minutes, just until the hominy is tender.
Finish soup: Add the chicken back to the pot. Season with plenty of salt, pepper, cayenne pepper and/or lime juice to taste.
Add toppings! Serve the pozole in bowls with desired garnishes such as cabbage, radishes, lime juice, avocados, cilantro, sour cream, tortilla chips, etc. Dig in!