Roast the chickens: Heat the oven to 400°F. Pat both chickens very dry. Rub each chicken with half the amount of rub. Ensure you get into all the crevasses, into the cavities and under the skins. Cook until the internal temp is around 160-167F.
Rest, pull and reserve: Rest the chickens 20 minutes. Pull all the meat, shred it into bite-size pieces, and refrigerate it. Keep every bone, the skin scraps and the pan drippings.
Char the stock vegetables: Set a rack close to the broiler or heat a dry cast iron pan over high heat. Char the cut sides of the yellow onion, 6 garlic cloves, unpeeled, and the thick fennel stems and trimmings from the fennel bulb until blackened in spots. Aim for dark and smoky, not burnt through.
Build the stock: Add all stock ingredients to a large pot. Cover with water.
Simmer and strain: Bring to a bare simmer, skim any foam, and cook uncovered, with no hard boiling, until the stock is rich and reduced, about 3.5 hrs. Strain through a fine sieve and discard the solids. Skim off the fat. Reduce further to get about 3 quarts of stock.
Sweat the vegetables: In a clean Dutch oven over medium heat, warm olive oil. Add carrots, sliced celery stems, yellow onion, and the diced fennel. Cook, stirring, until softened and the fennel and onion are just turning translucent. Add the minced garlic and smoked paprika until fragrant
Toast the flour and paprika: Sprinkle in all-purpose flour and cook, stirring, until it smells nutty and no dry flour remains.
Add stock and simmer: Gradually whisk in the strained stock (about 3 quarts), scraping up anything stuck to the bottom. Bring to a simmer and cook until the vegetables are tender and the broth has a little body.
Finish: Stir in the shredded chicken, the chopped parsley leaves. Simmer just until the chicken is heated through. Taste and adjust the salt and pepper. Serve hot, topped with a few reserved fennel fronds.