3 plum tomatoes, halved lengthwise
1/4 cup extra-virgin olive oil
One 3 1/2-pound chicken, cut into 8 pieces
1 medium Spanish onion, finely chopped
1 medium green bell pepper, finely chopped
5 garlic cloves, minced
4 thyme sprigs
1 bay leaf
1/2 teaspoon sweet pimentón de la Vera (smoked Spanish paprika)
1/2 pound oyster or cremini mushrooms, cut into 1-inch pieces
3 cups water
1 cup Bomba or Calasparra rice
Small pinch of saffron threads
Hot sauce, for serving
Working over a bowl, grate the cut side of the tomatoes on the large holes of a box grater; discard the skins.
In a very large, deep skillet, heat the olive oil until shimmering. Season the chicken with salt and pepper, add it to the skillet skin side down and cook over moderate heat, turning once, until nicely browned on both sides; transfer the chicken to a plate.
Pour off all but 2 tablespoons of the fat from the skillet. Add the onion and green pepper, season with salt and cook over moderate heat, stirring occasionally, until just starting to brown, 10 minutes. Add the garlic, thyme sprigs, bay leaf and pimentón and cook, stirring, until fragrant, 2 minutes. Add the grated tomatoes and cook, stirring, until the liquid has evaporated, about 5 minutes. Stir in the mushrooms and cook over moderately high heat until they start to soften, 3 minutes.
Add the water to the skillet and bring to a boil. Stir in the rice, saffron and a generous pinch of salt and return to a boil. Nestle the chicken in the rice and cook over moderately low heat, without stirring, until the rice is tender and the chicken is cooked through, 20 to 25 minutes. Discard the thyme sprigs and bay leaf. Season the dish with salt and pepper and serve with hot sauce.