1 Turn on the broiler: Set an oven rack about 4 inches from the broiler element. Turn on the broiler.
2 Broil the tomatillos, poblano chile(s), and garlic: Remove the husks from the tomatillos and rinse them under cool running water to remove the sticky residue. Lightly oil a rimmed baking sheet, then place the tomatillos, chile(s), and garlic on top. Broil for 4 to 5 minutes on a side, or until the skins are splotchy with black spots and the tomatoes are soft. Cool briefly.
3 Make the sauce: Scrape away any loose blackened skin from the chile(s). (Don’t worry if you can’t scrape off all of it.) Cut in half and remove the seeds. Combine the broiled tomatillos, chiles, garlic, onion, cilantro, salt, and the accumulated juices from the baking sheet in a blender. Pulse until you obtain a coarse puree. Set aside. (Sauce can also be prepared a few days ahead and kept refrigerated.)
4 Prepare the chicken: Preheat the oven to 375°F. Sprinkle the chicken thighs on both sides with salt and pepper.
5 Brown the chicken: In a large ovenproof skillet over medium-high heat, heat the olive oil. Add the chicken thighs with the skin side down. Cook for 6 to 8 minutes, or until the skin is golden brown and crisp. Transfer to a plate.
6 Begin cooking the peppers and potatoes: Pour off all but a thin layer of fat from the pan. Return the pan to the heat and add the potatoes, peppers, and 1/4 cup of the water. Cook, stirring occasionally, for 8 minutes, or until the potatoes are almost tender. If the vegetables start to stick to the bottom of the pan, add more water, 2 tablespoons at a time.
7 Add the sauce and chicken to the pan: Stir the tomatillo sauce, corn, and stock into the skillet. (If you’re using fresh corn, you can reserve some of it for garnish, if you like!) Bring to a simmer and taste. Add more salt and pepper, if you like. Nestle the chicken into the skillet with the skin side up. The chicken should be partially submerged, with the skin rising above the sauce.
8 Bake the chicken: Bake for 20 minutes, or until a thermometer inserted into the thickest part of a thigh registers 165F. Remove from the oven.
9 To serve: Spoon the vegetables and sauce into 4 shallow bowls and top each with 2 chicken thighs. Sprinkle with cilantro. Garnish with lime wedges and serve with rice or tortillas, if you like.