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Step 1
Pull off the husks of the tomatillos and give them a good rinse. I usually de-stem them but this is optional. Add the tomatillos to a roasting pan along with the rinsed poblanos and roast them in the oven at 400F. I usually flip the poblanos over after 15-20 minutes, and if the tomatillos are disintegrating you can take them out of the oven at this point. The poblanos will need about 30 minutes total to fully roast.
Step 2
Add the two chicken breasts to a pan and cover with 2 quarts of stock. Be sure there is enough liquid to submerge the chicken breasts. I also added 1/2 onion, 10 sprigs cilantro, a pinch of salt, and some freshly cracked black pepper but these are optional.  Bring to a boil and then reduce heat to a simmer. Cook the chicken until no longer pink inside, about 20 minutes. Once cooked, set the chicken aside to cool on a plate and then shred using two forks.  Save the cooking liquid.
Step 3
Add the remaining green sauce ingredients to a blender: 1 peeled onion, 2 de-stemmed and rinsed jalapenos, 4 peeled garlic cloves, and 1/2 bunch of rinsed cilantro. I usually just twist off and discard the bottom, thicker portions of the cilantro but use the upper stems that hold the leaves together.
Step 4
Once the poblanos have fully roasted, remove them from the oven and let them cool down for a few minutes. Pull off and discard as much of the skin as you can. De-stem and de-seed them. I find it easiest to cut off the tops and then make a slit lengthwise. Open up the pepper and use the knife to scrape out the veins and seeds.
Step 5
Add the poblanos and tomatillos to the blender and combine well with the other ingredients. You might have to blend half first to get all of it to fit into a single blender.
Step 6
Add a dollop of oil to saucepan or Dutch oven over medium heat. Add the green sauce from the blender and cook for a few minutes.
Step 7
Drain and rinse 2 cans of hominy. If you want a soupier version then use only a single can. Add the hominy to the green sauce.
Step 8
Add the shredded chicken to the pan along with the chicken cooking liquid (I gave the cooking liquid a quick strain to remove the onion and cilantro bits).  We'll also add 1 teaspoon Mexican oregano, 1 teaspoon salt, and some freshly cracked black pepper. You can always add additional liquid at this point if you want a thinner version (stock or water).
Step 9
Let simmer for 15 minutes or until the hominy is heated through. Take a final taste for seasoning, adding more salt if necessary.
Step 10
Serve immediately with a squeeze of lime. You can optionally serve it with a cheese quesadilla. Simply add cheese to half of a flour tortilla and fold onto itself. Cook in a dry skillet over medium-high heat until both sides are crispy and golden brown.
Step 11
Store leftovers in an airtight container in the fridge.