Preheat the oven to 425 degrees F.
Score the tomatillos (i.e. cut a small slit in the bottom of each). Arrange them along with the jalapenos on a parchment-lined baking sheet. Roast in the oven, turning once 15 minutes in, until charred and soft, about 30 minutes. Set aside to cool.
Meanwhile, make the stew: in a large Dutch oven or stock pot, heat 1 tablespoon of olive oil. Season the chicken with sea salt and sear over high heat until nicely browned, about 4 minutes on each side. Remove to a plate.
Add the onions to the pan and sauté, scraping up any brown bits that formed on the bottom, until translucent, 5 minutes. Add the garlic, cumin, and 1 teaspoon sea salt. Cook one minute more. Arrange the chicken in the bottom of the pot.
Remove the skins from the jalapenos and add to the chicken along with the tomatillos.
In a small mixing bowl, whisk together the cornstarch and ½ cup of stock until dissolved. Add this “slurry” to the pot along with the remaining stock. Bring to a boil, reduce the heat, and simmer until the sauce has thickened, about 20 minutes.
Remove the chicken to a plate or cutting board and shred.
Puree the sauce with an immersion or stand blender until semi-smooth. Return the chicken to the pot and add the cilantro and lime juice. Taste for seasoning.
Serve the chicken chile verde over brown rice or quinoa with a dollop of Greek yogurt or sour cream.