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

Transfer the charred ingredients to a bowl and cover with plastic wrap to steam for about 10 minutes. Peel off the skins and remove the stems and seeds from the peppers. Peel the garlic cloves.

Place the peeled peppers, tomatillos, onion, and garlic into a food processor and pulse until finely chopped to create 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 for an additional 30 minutes.

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