Feel free to cook the chicken any way you want, but for this batch I brined and baked it. To brine the chicken, add 1/2 cup Kosher or sea salt to 2 quarts of water in a mixing bowl. Stir to dissolve the salt and add the chicken breasts, letting them brine in the fridge for 30-60 minutes. If the chicken isn't fully submerged then add a bit more water. Once brined, pat dry the chicken and add it to a baking sheet.
Pull off the husks of the tomatillos and give them a good rinse. I usually de-stem them too. Add the tomatillos to the baking sheet along with the rinsed poblanos and the brined chicken. Roast everything in the oven at 400F.
If you're cooking rice from scratch for your burritos now's a good time to start it. Add a single cup of uncooked white rice to a saucepan along with a glug of oil. Let the rice cook over medium heat until it's turning opaque and light brown in color, stirring occasionally. Add 1.5 cups water (or stock) along with 1/2 teaspoon salt. Bring to a boil, then reduce heat to a simmer, cover, and let cook until all the liquid is absorbed. Once cooked set it aside on the stove and let it sit in its own steam for a few minutes, covered.
Cook the chicken until it registers 160F or until the insides are no longer pink -- this usually takes 20 minutes but sometimes it will take a couple extra minutes if there was an extensive brine. Remove the chicken once cooked and let the poblanos and tomatillos roast for a bit longer or until you need them. I usually cover the cooked chicken breasts with foil and let them rest a bit before shredding.
Once roasted you can de-stem and de-seed the poblanos. Add the roasted poblanos and tomatillos to a blender along with 1/2 onion, 4 peeled garlic cloves, 15-20 cilantro sprigs, and 1-4 rinsed, de-stemmed jalapenos. If you want a milder batch start with a single jalapeno, combine, and take a taste for heat level, adding more jalapeno to increase the heat. I used 3 jalapenos for this batch and it had some zip!
Simmer the blended green sauce in a glug of oil (or lard, or bacon drippings) over mediumish heat. Add 1 tablespoon Mexican oregano, 1/2 teaspoon cumin (optional), 1/2 teaspoon salt (optional), and some freshly cracked black pepper. Taste for seasoning. Note: if you brine the chicken you probably won't need to add much additional salt.
Use two forks to shred the chicken breasts and then add it to the Chile Verde sauce. Combine well over medium heat. Once everything is up temp it's ready to serve.
To make the Salsa de Aguacate, add the following ingredients to a blender or food processor: the flesh of a ripe avocado, 1/4 cup water, the juice of 1 lime, 4-5 sprigs of cilantro, 1/2 peeled garlic clove, and 1/4 teaspoon salt. Combine well. If it's not combining readily simply add another splash of water. Note: don't fret if the Salsa de Aguacate has a subtle, light flavor out of the blender as it will come alive when paired with the chicken.
To build the burritos, start by warming up a flour tortilla. Add a thin layer of rice, cheese, and plenty of Chicken Chile Verde to the tortilla. Roll tight. Crisping up your burritos is a must so no skipping this step! You can crisp them up in dry skillet over medium heat if you want. But for this batch I added a drizzle of bacon drippings to the skillet to help crisp them up even further. Give them a minute or so on each side, or until they are turning medium brown in color. You could also use lard in place of the bacon drippings.
Serve your crispy burritos immediately along with plenty of the Salsa de Aguacate.
Store leftover Chicken Chile Verde in the fridge where it will keep for days at a time. The Salsa de Aguacate won't last as long but I usually get a couple days out of it when there are leftovers.