Preheat the broiler to high. Arrange the poblano peppers, Anaheim peppers, tomatillos, sliced onion, and garlic cloves on a rimmed baking sheet. Drizzle lightly with vegetable oil. Place under the broiler, turning occasionally, until the peppers are charred on all sides and the tomatillos are softened, about 8-10 minutes.

Transfer the charred peppers to a bowl and cover tightly with plastic wrap to steam for about 10 minutes. Once cooled, peel off the skins, remove the stems and seeds from the peppers. Peel the garlic cloves from their skins.

Place the peeled peppers, tomatillos, onion, and garlic into a food processor and pulse until finely chopped, creating a chunky green sauce.

Transfer the green sauce mixture to the slow cooker. Add the chicken broth, chicken breasts, cumin, oregano, chili powder, and kosher salt. Stir to combine gently.

Cover and cook on high for 4 to 6 hours, until the chicken is tender and cooked through.

Using two forks or tongs, break up the cooked chicken into bite-sized pieces. Stir in the drained hominy and cook the mixture for an additional 30 minutes to meld flavors and heat through.

Taste the posole and adjust seasoning if needed. Serve hot with garnishes of sliced radishes, fresh cilantro sprigs, lime wedges, and cubed avocado.