Heat oil in a medium Dutch oven over high heat until it simmers. Pat the chicken dry with paper towels; season with salt and pepper. Place chicken in the pan, in batches, top-side-down. Cook until golden brown, 4 minutes. Turn over, continue cooking 3 minutes. Remove chicken to a plate.
Add peppers and cook, stirring occasionally, until slightly soft, about 5 minutes. Add garlic and cook for 1 minute. Add tomato paste and cook for 1 minute. Add the vinegar and cook until reduced by half. Add honey and broth, season with salt and pepper to taste and cook for 5 minutes. Return the chicken and accumulated juices to the pot. Reduce heat to medium, cover the pot and cook until the chicken is tender, about 15 minutes. Remove the chicken to a platter. Cook sauce until slightly reduced, about 5 minutes. Stir in parsley and pour the sauce over the chicken.