Make the stock: Combine the chicken wings, onion, celery, carrots, bay leaves,thyme, and peppercorns in a stock pot. Cover with water. Bring to a simmer and simmer, uncovered, for 1 hour. Add the saffron threads and simmer 15 additional minutes.

Strain the stock by pouring it through a fine strainer. Discard the solids. Let cool and refrigerate if not using immediately.

While the stock is cooking, remove all meat from the roasted chicken, shredding as you go. Refrigerate until ready to use.

Make the sauce: Place the tomato paste, catsup, and smoked paprika in a blender. Add 2 cups of the stock and puree until smooth.

Finish the chicken: Heat the vegetable oil in a large skillet over medium heat. Add the sliced onion, bell peppers and garlic and cook until translucent. Add the pureed sauce and cook, stirring until the sauce thickens, about 8 - 10 minutes. Add the shredded chicken and stir to coat. Season with salt and keep warm.

Make the paella: Preheat the oven to 350°F.

Heat the olive oil in a paella pan or large ovenproof skillet over medium-high heat. Add the chorizo and cook until the fat renders, about 5 minutes. Add the diced onion and garlic and cook until the onion is translucent, about 10 minutes.

Add the rice and stir lightly to coat with the oil, about 5 minutes. Stir in the peas, piquillo peppers, olives,chicken mixture, and 3 cups chicken stock. Season with salt.

Cover tightly with foil and bake until the liquid is absorbed, about 45 minutes. Remove from the oven, mix in the shrimp and let rest 5 minutes. Serve in the pan.