Heat a large pot over high heat and add 1 tablespoon olive oil. Season the chicken with salt, pepper and 1 teaspoon cumin. Working in batches if necessary, add the chicken to the pot and cook until golden, 4 to 5 minutes per side. Remove to a plate.
Add the remaining 1 tablespoon olive oil, the onion and poblano to the pot and cook, stirring occasionally, until softened, about 2 minutes. Add the garlic and remaining 1 teaspoon cumin; cook until golden, 30 seconds. Stir in the chicken broth, collards, chili beans and tomatillos. Stir in the chicken and any juices from the plate. Cover and bring to a boil, then uncover and reduce the heat to a steady simmer. Cook until the chicken is tender, about 15 minutes.
Shred the chicken in the pot with 2 forks. Divide the chili among bowls and top with the scallions.