Season the chicken with salt and pepper. Heat the oil in a large pot over medium-high heat. Brown the chicken in batches, 3 to 4 minutes per side; remove. Add the onion, garlic, poblanos, jalapeño and cilantro. Cook until softened, 6 minutes. Add the cumin, coriander, chile powder and 1/2 teaspoon salt and cook, stirring, 1 minute.
Add 2 cups water, the chicken broth, chicken and green chiles. Bring to a simmer and cook, adjusting the heat as needed and stirring occasionally, until the chicken is tender, 20 minutes. Remove the chicken, shred and return to the pot along with the beans. Simmer until thickened, 30 to 40 minutes. Season with salt and pepper.