How to Make It
Using sturdy kitchen shears, cut along both sides of the backbones of both chickens. Remove the backbones and cut each one into 3 pieces. Cut off the chicken wing tips, then cut each chicken into 8 pieces.
Put the backbones and wing tips in a large saucepan along with the reserved necks, gizzards and hearts. Add the carrot, shallot and water, cover and bring to a simmer over moderately low heat. Cook until the water is reduced to 3 cups, about 1 hour. Strain the broth, pressing hard on the solids to extract as much liquid as possible.
Meanwhile, bring a medium saucepan of water to a boil. Add the potatoes and cook until just tender, about 25 minutes. Drain the potatoes and let cool slightly, then peel them. Cut the potatoes in half if they seem large.
Heat 2 tablespoons of the olive oil in a large skillet until shimmering. Add the potatoes and cook over moderately high heat, stirring occasionally, until golden all over, about 5 minutes. Transfer the potatoes to a large plate. Add 2 more tablespoons of the olive oil to the skillet and heat until shimmering. Add the zucchini and yellow squash chunks, season with salt and pepper and cook over high heat, stirring occasionally, until golden and just tender, about 5 minutes. Add the vegetables to the potatoes on the plate.
Pierce the chorizo and add it to the skillet. Cook the chorizo over moderately high heat, turning, until browned all over, 8 to 10 minutes. Drain on paper towels and cut it into 1/4-inch slices.
Season the chicken pieces with salt and pepper. Spread the flour on a plate. Add the chicken, a few pieces at a time, and coat with the flour, shaking off any excess. Heat 1/4 cup of the olive oil in a large skillet until shimmering. Add half the chicken pieces to the skillet and cook over moderately high heat until crisp and golden all over, about 8 minutes; transfer to a large platter. Repeat the process with another 1/4 cup of olive oil and the remaining chicken.
7. Heat the remaining 2 tablespoons of olive oil in a large enameled cast-iron casserole. Add the red bell peppers, onion and garlic and cook over moderately low heat, stirring often, until softened, 8 to 10 minutes. Raise the heat to moderately high and add the tomatoes, white wine, bay leaves and thyme sprig. Simmer the mixture until the liquid is nearly evaporated, about 5 minutes. Add the browned chicken pieces along with the reserved 3 cups of broth and bring back to a simmer. Cover partially and cook over low heat until the chicken is tender when pierced with a fork, about 45 minutes.
Add the cooked chorizo to the casserole and cook for 5 minutes. Stir in the cooked potatoes, zucchini and squash and cook over moderate heat until warmed through, about 5 minutes. Transfer the ragout to a platter and serve.