Season both sides of the chicken with salt and pepper. Next, heat 2 TBSP of oil in a large pot over medium-high heat and brown the chicken in batches if necessary, to avoid overcrowding. 

Then, add the water, remaining browned chicken, allspice, onion, garlic cloves, and bay leaf to the pot. Bring to a boil, reduce heat to medium-low for a gentle simmer, cover, and cook for 20-25 minutes or until the chicken is fully cooked. 

Preheat the oven to high broil. 

Arrange the tomatillos, peppers, onion, and garlic in a single layer on a parchment-lined sheet pan. Drizzle with oil. Broil for 10-15 minutes, or until the surface has blistered and blackened.

Meanwhile, if the chicken is done, remove it from the broth and let it cool slightly. Then, carefully strain the broth and set it aside.

Once the roasted ingredients are done, remove them from the oven and let them cool. When the chicken is cool enough to handle, shred it and discard the bones and skin.

Transfer the roasted ingredients to a blender, peeling the garlic cloves and removing the skin from the poblano peppers first. Add the broth and blend until smooth. Set aside temporarily.

Heat a large pot over medium heat with 2-3 TBSP of oil. Sauté onions until lightly browned, then add garlic, oregano, cumin, and tomato paste. Cook 1 minute. Stir in salsa verde and chicken broth. 

Refrigerate excess broth for later use.

Simmer covered for 10 minutes. Then, add the pinto beans, corn, shredded chicken, and cilantro; stir. Continue simmering, covered, 10 more minutes or until desired thickness is reached. 

Finish with a lime juice and salt. Serve immediately, garnished with a dollop of sour cream, grated cheese, and fresh green onions.