How to Make It
Heat oil in a deep 10 1/4-inch to 12-inch heavy-bottomed skillet over medium-high until hot and fragrant. Pat chicken dry. Season skin side of chicken evenly with 1 teaspoon salt, and place chicken, skin side down, in hot skillet; it should sizzle immediately. Cook, undisturbed, until well browned, 10 to 12 minutes. Sprinkle evenly with 1/2 teaspoon salt. Flip chicken, and cook, undisturbed, until browned on bottom, 4 to 5 minutes. Transfer to a plate.
Pour off all but 2 tablespoons drippings from pan, taking care not to pour off any of the flavorful browned bits. Return pan to heat over low; add onion, black pepper, and remaining 1/4 teaspoon salt. Cook, stirring often, until onions are meltingly tender and beginning to caramelize, about 20 minutes, stirring in garlic during final 5 minutes of cook time. Stir in coriander and pimentón; cook, stirring constantly, until fragrant, about 1 minute. Deglaze with wine, and increase heat to medium. Cook, stirring often, until wine is almost completely absorbed, about 2 minutes. Stir in chicken stock and lemon zest. Return chicken, skin side up, to pan along with any juices. Bring to a simmer over medium-high. Reduce heat to low; cover and gently simmer until chicken is cooked through, 10 to 12 minutes, stirring in olives and apricots halfway through cooking time, making sure apricots are submerged in liquid.
Transfer chicken to a serving platter. Add butter to pan (liquid doesn’t have to be simmering), whisking constantly to incorporate. Serve chicken with sauce.