Set oven to broil on high. Place Hatch green chiles and halved tomatillos cut-side down on a foil-lined baking sheet. Broil for 8 to 10 minutes until tomatillos are soft with deep char and chiles are blistered all over.

Transfer chiles to a bowl and cover tightly with plastic wrap. Let steam for 10 minutes, then peel, seed, and roughly chop them.

Add tomatillos and their juices to a blender and pulse into a rough, chunky salsa. Set aside.

Season chicken thigh chunks generously with salt, pepper, and half the cumin.

Heat olive oil in a large Dutch oven over medium-high heat. Brown chicken in a single layer for 3 to 4 minutes per side without moving. Work in batches. Remove and set aside.

In the same pot, cook diced onion over medium heat for 5 minutes, scraping up browned bits. Add garlic, remaining cumin, and oregano. Cook 2 more minutes until fragrant.

Pour in the blended tomatillo mixture. Add chopped roasted chiles, chicken broth, and browned chicken with any resting juices. Stir to combine and bring to a gentle boil.

Reduce heat to low, cover partially, and simmer for 35 to 40 minutes until chicken is tender and pulls apart easily.

Add drained white beans in the last 15 minutes. To thicken, mash a handful of beans against the side of the pot with the back of a spoon.

Taste for salt. Squeeze in juice of half a lime just before serving. Serve with fresh cilantro, lime wedges, and warm flour tortillas.