Wash the chicken quarters well under cold running water and place in a large (6-quart) saucepan. Add 6 cups of water.

In a blender, combine the chopped onion, garlic, cumin, salt, black pepper, and 1/4 cup water. Place the lid of the blender on tightly and blend on high speed until the mixture is liquefied and smooth, about 2 minutes.

Add this flavoring mixture to the pot with the chicken, and place the pot over high heat. Bring to a boil, skim any foam that rises to the surface, and reduce the heat to medium-low so that the liquid boils gently. Continue to cook, uncovered, for 45 minutes, until the chicken is very tender.

Remove the chicken quarters from the cooking liquid with tongs, place on a large plate or baking sheet, and set aside to cool. Strain the cooking liquid through a fine-mesh sieve into a medium mixing bowl and discard the solids. Return 4 cups of the cooking liquid to the saucepan and reserve any remaining cooking liquid on the side.

When the chicken has cooled enough to handle, discard the skin and bones and tear the meat into bite-size pieces. Set aside. Wash your hands well before proceeding.

Add the olive oil and saffron to the 4 cups of cooking liquid in the saucepan and bring to a boil over high heat. Add the rice and stir to combine. When the liquid returns to a boil, stir the rice once more, then cover the saucepan, and reduce the heat to medium-low. Cook the rice, undisturbed, for 20 minutes, until it is tender and has absorbed the cooking liquid. Set aside.

While the rice is cooking, heat a large nonstick skillet over medium-high heat and add the butter. When the butter has melted, add the sliced onion, bell peppers, olives, and capers, and cook for 2 minutes, until the vegetables are just beginning to soften. Add the reserved chicken and the soy sauce, and continue to cook over medium-high heat, stirring occasionally, until the vegetables are soft and the flavors have blended, about 15 minutes. If the mixture begins to stick before the vegetables are soft, add a bit of the reserved cooking liquid to the pan and stir to release any bits stuck to the bottom. Set aside.

When the rice is cooked, add the chicken mixture to the pot with the rice and stir gently to combine. Cover the pot and allow the mixture to sit for 15 to 20 minutes to allow flavors to blend. Garnish with the chopped green onions and cilantro and serve.