First, turn on your oven to 425°F (218°C) with a sheet pan inside. Let it come to temp and get everything nice and hot for at least 30 minutes.
While the oven and pan are heating up, clean your tomatillos, slice your peppers in half and remove their seeds, and cut your onion into 6ths. Drizzle them with oil and toss to coat. Set aside until ready to cook in the oven.
Then, take out your blender and set it aside on the counter with the lid off. Next, toast your spices in the pot that you are going to cook your pozole in. Turn your burner on medium-high and toss in the black peppercorns, coriander, and cumin. Move the spices around the pot by shifting it back and forth every 30 seconds or so. Once you can smell the spices, take them off the burner and dump them into your open blender.
Add in salt and the middle ⅓ of your cilantro bunch as well as the roasted (see FAQ for roasted garlic info) or fresh garlic and lime juice.
Your oven and pan should be properly pre-heated by now. Carefully pull the pan out of the oven and add the prepped peppers, onions, and tomatillos onto it. Place it back into the oven and let them roast for 10-15 minutes. Then, turn your oven to broil and let them char for another 5 minutes.
Take the roasted ingredients out of the oven and use tongs to add everything to the blender. (see notes about peeling peppers) Blend until smooth and then pour your salsa verde into a separate pot or large saucepan. Cook the salsa on medium until it darkens a bit, about 5-10 minutes. (this deepens the flavor even further) Then pour the cooked salsa verde into the pot with chicken stock to combine them. Now, you can add in your hominy and the shredded chicken. Warm everything through on the stove top for 15 minutes.
While the soup is warming, prep whatever toppings you’d like to use. I like sliced radishes, shredded cabbage, and cilantro leaves. (see FAQ for more options) Once done, salt to taste and ladle yourself a bowl of pozole verde. Lastly, add your preferred toppings and enjoy!