In a large pot over medium-high, heat the oil. Add the onion, season with salt and cook, stirring just a few times, until translucent and browned, 6 to 9 minutes. Add the peppers, tomato paste, brown sugar and cumin, and cook, stirring constantly, until the paste is a shade darker and starts to stick to the bottom of the pot, 2 to 3 minutes.
Step 2
Add the broth, chicken, greens and pickled-pepper brine. Season with salt and stir to combine. Cover the pot, keep on medium-high and bring to a simmer. Uncover, reduce heat to low, and cook uncovered until the chicken is cooked through and the greens are tender, 15 to 20 minutes. Using two forks, shred the chicken right in the pot into pieces, then stir to combine. Taste and adjust with salt, sugar (if it’s too tangy or spicy) and brine (if it’s too sweet or flat). Eat with starch of choice.