Line a baking sheet with parchment paper. Place lightly oiled Hatch peppers or poblano, quartered onions, jalapeños or serrano peppers on the baking sheet. Set the tray directly under the broiler on high heat. Broil for 5 minutes, or until the skin is charred and blistered. Carefully flip over the onions and peppers, broil for another 5 minutes, or until the skin is blackened and blistered on all sides.
Remove from the oven, loosely cover to keep the steam in for 5 minutes. Remove the skin off the peppers as much as possible, they usually slip off easily. Chop and save with its juice.
Bring a pot of water or broth to boil with the tomatillo just enough to cover them. Steam for 5 minutes so they're just soft. Lift the tomatillos out, save the water, Dice the onions add it to a blender along with minced garlic, hatch peppers, cilantro, tomatillo and jalapeño. Blend until smooth. Set aside until ready to use.
Heat olive oil in a large pot over medium-high heat. Add the chicken and season with salt, ground cumin and oregano. Sear the chicken on all sides, turning occasionally. Add the potato, broth saved from the tomatillo as needed and bring it to a gentle simmer. Cook for 25-30 minutes until the chicken is fully cooked.
Pour in the chile verde sauce and white beans. Mix thoroughly. Cover, bring it to a simmer for 5-7 minutes, add more broth if needed. Turn the heat off add the lime juice stir to combine. Taste and season if needed. Serve with garnishes, steamed rice and tortilla chips.