Disjoint the chicken, reserving the back and neck.

Trim off some of the fat, but leave the skin intact.

Chop the chicken with a cleaver into 12 to 24 small pieces, being careful of bone shards.

In a stockpot, heat 1 tablespoon of olive oil over medium heat.

Add the chicken back, neck, one third of the onion, and the carrot and cook until they begin to brown, about 5 minutes.

Reduce the heat to low and cook for another 5 minutes, until they release their juices.

Add the celery, parsley stems, bay leaf, peppercorns, 2 pinches of salt, and the water.

Bring to a boil, reduce the heat, and simmer, covered, for 45 minutes.

Strain and reserve the liquid, discarding the solids.

Season the chicken generously with salt and pepper.

In a large cazuela or Dutch oven, heat the remaining 3 tablespoons of olive oil over medium heat.

Add the chicken pieces and cook until browned, about 5 minutes.

Transfer the browned chicken to a platter.

Prepare the sofrito in the same pan.

Reduce the heat to medium-low, add the remaining onion, and cook, stirring frequently, until softened and nearly translucent, 5 to 10 minutes.

Add the tomatoes and 2 pinches of salt and cook, stirring from time to time, until the tomato has darkened to a deeper shade of red and the sofrito is pasty, 10 to 15 minutes.

Return the chicken to the cazuela along with any juices from the platter, add 1 cup of liquid from the stockpot, and let simmer slowly over low heat for 15 minutes, or until the stock is ready.

Meanwhile, prepare the picada by pounding in a mortar the garlic and parsley leaves with 2 tablespoons of stock until you have a fine paste.

Alternatively, whir them in a food processor or blender.

Sprinkle the pimenton and saffron into the cazuela, letting the flavors meld for a few seconds while stirring constantly.

Add the remaining 8 cups of stock, increase the heat, and bring to a boil.

Add the rice and spoon in the picada.

With a wooden spoon, probe the pan to make sure the rice is evenly distributed.

Cook, uncovered, over medium-high heat for 10 minutes, gently stirring occasionally.

Check for salt, adjusting the seasoning as needed.

Reduce the heat to low and cook for an additional 8 minutes, or until most of the liquid is absorbed and the rice is al punto, with just a bite to it.

Remove the cazuela from the heat and immediately transfer the food to plates, letting the rice rest for a few minutes before serving.