Stir together paprika and oregano. Arrange chicken on a large rimmed baking sheet and season with 2 tablespoons salt, then the spice mixture (use all of it). Set aside at room temperature (or refrigerate chicken, uncovered, overnight).
Preheat the oven to 325°F. Drain tomatoes and tear them into 4 or 6 strips each, transferring to another large rimmed baking sheet as you go. Drain and rinse chickpeas; add to baking sheet. Add the thyme, bay leaves, and chiles, scattering them about. Season with salt and pepper, then pour over ½ cup oil and stir to coat. Bake until tomatoes are shrunken and look a bit dried out, and chickpeas are starting to turn golden brown, 1 hour, stirring once halfway through (this cooks off some moisture in the tomatoes so they’ll get nice and jammy by the end).
Meanwhile, peel the onion and cut into ¼-inch wedges. Lightly crush the garlic cloves. Add the onion and garlic to tomato-chickpea mixture. Nestle in chicken, skin side up, then pour over the remaining ¾ cup oil. Bake until the skin is browned and the meat is tender enough to shred with a fork, 1½ hours. If chicken isn’t done, bake for 15 minutes more, then check again. Go longer if needed.
Transfer chicken to a large platter. Pluck out bay leaves and thyme sprigs. Using a slotted spoon, spoon tomatoes and chickpeas around chicken. Pour cooking liquid from baking sheet into a glass measuring cup; let settle for a few minutes. Pour most of the oil that rises to the top of the liquid into a clean jar or bowl, then spoon remaining chicken-y juices over the platter. (Cover and refrigerate the extra confit oil; use it the next time you make beans, soup, or roast vegetables.) Season the chicken with a few dashes of vinegar before serving.
Reprinted from That Sounds So Good by Carla Lalli Music. Copyright © 2021 by Carla Lalli Music. Photographs copyright © 2021 by Andrea Gentl and Martin Hyers. Published by Clarkson Potter, an imprint of Random House, a division of Penguin Random House LLC.