To brine the chicken, add 1/4 cup salt to a quart of water in a mixing bowl. Dissolve the salt and add the chicken breasts, letting them brine covered in the fridge for 30 minutes or so. If the chicken breasts aren't fully submerged then add a bit more water. Once brined, pat dry the chicken breasts and add them to a baking sheet.
Rinse and de-stem the tomatoes and tomatillos. Add them to the same baking sheet and bake everything at 400F for about 20 minutes or until the chicken is no longer pink inside (160F).
Once the chicken has cooled a bit you can shred it with two forks and set aside until you need it.
Meanwhile, roughly chop a half onion and saute in some oil over medium heat. Add 4 whole, peeled garlic cloves and saute until the onion is starting to brown.
Add the onion-garlic mixture to a blender along with 3 chipotles in adobo and the roasted tomatoes and tomatillos. I usually scrape out the seeds of the chipotles. Combine well and take a taste, adding more chipotles if you want more heat.
Add the Tinga mixture back to the same pan you used to cook the onion. Add 1 teaspoon Mexican oregano, a pinch of cumin (optional), 1/2 teaspoon of salt, freshly cracked black pepper, and 1-2 tablespoons of adobo sauce (optional). Bring to a simmer and take a final taste for seasoning.
Add the shredded chicken to the Tinga sauce and let simmer until everything is at a uniform temp. Serve as you see fit, with these Tinga Tacos and these Tinga Tostadas being good options. Store leftovers in an airtight container in the fridge.