Set your oven to broil on high and move a rack to the top position. Place the whole tomatillos and the whole poblano pepper on a rimmed baking sheet. Drizzle the tomatillos with the olive oil and toss to coat. Broil for 5 to 7 minutes, turning the poblano with tongs halfway through, until the tomatillos are soft and lightly charred in spots and the poblano skin is blistered and dark on most sides. The tomatillos will release some juice and look slightly collapsed, which is exactly what you want.

Transfer the poblano to a small bowl and cover it tightly with plastic wrap or a plate. Let it steam for 10 minutes, which makes the skin easy to peel. After resting, peel away and discard the charred skin, then pull out and discard the stem and seeds. Rough chop the peeled poblano flesh.

Add the broiled tomatillos and all their juices from the baking sheet to a blender. Add the chopped poblano, half of the chopped white onion, the garlic cloves, cilantro, cumin, salt, and black pepper. Blend on high for about 30 seconds until the sauce is smooth and bright green. Taste it at this point. It should be tangy and savory with a mild heat. Set the verde sauce aside.

Place the chicken thighs into the Instant Pot insert in a single layer as best you can. Pour the verde sauce over the chicken, then add the remaining half of the chopped onion, the drained hominy, and the chicken broth. Stir everything gently to combine. The liquid should come about halfway up the insert. Make sure you are not above the max fill line.

Secure the Instant Pot lid and set the valve to the sealing position. Select Pressure Cook or Manual on High pressure and set the time to 20 minutes. The pot will take about 10 minutes to come to full pressure before the timer starts. While the soup cooks, prep your toppings: slice the avocado, shred the cabbage, cut lime wedges, and warm the tortillas in a dry skillet or wrapped in a damp paper towel in the microwave.

When the 20 minutes are up, let the pressure release naturally for 15 minutes. You will see the float valve drop when it is fully depressurized. Then carefully turn the valve to venting to release any remaining steam before opening the lid. The broth will be a deep olive green and the chicken will look fully cooked through.

Use two forks or tongs to pull the chicken thighs out of the pot and onto a cutting board. Shred the meat into bite-sized pieces. It should pull apart easily with almost no effort. Return the shredded chicken to the pot and stir it into the broth. Add the lime juice, stir again, and taste the broth for salt. Add more salt or a little more lime juice if it needs brightening.

Ladle the posole into bowls and serve right away. Set out the sliced avocado, shredded cabbage, radishes, crema, and lime wedges so everyone can build their own bowl. Warm corn tortillas on the side are great for dipping or rolling up with the toppings.