Sherry vinegar, paprika, green olives,and jarred piquillo peppers provide Spanish flair for this deeply flavorful braise. It starts with a whole chicken cut into pieces.
Preheat oven to 400 degrees. Season chicken on both sides with salt and paprika. Heat an ovenproof 12-inch skillet or shallow braising pan over medium-high heat. Swirl in oil. Working in 2 batches, add chicken to pan and cook until well browned, about 2 minutes on each side, adding more oil as needed. Transfer chicken as it is browned to a plate.
Reduce heat to low and stir in garlic, then tomato paste, scraping up browned bits in pan with a wooden spoon. Return chicken to skillet, increase heat to high, and pour in vinegar. Boil, stirring, until reduced to a glaze.
Stir in broth and bring to a boil. Add peppers and olives. Transfer to oven and braise until a thermometer inserted into thickest part of breast (do not touch bone) reaches 160 degrees and liquid is reduced by half, 20 to 25 minutes. Garnish with parsley.