In a small bowl, rehydrate the porcini in the warm water for 30 minutes. Lift the porcini out with a slotted spoon and chop finely. Strain the liquid through a double thickness of damp paper towels to catch any grit. Reserve the porcini and liquid separately.

Season the chicken with salt and pepper. Heat a large skillet over high heat. Coat with a thin film of olive oil, then add the chicken, skin side down. Brown well on the skin side, 8 to 10 minutes, reducing the heat if necessary to keep the chicken from burning. Turn and cook for about 2 minutes on the second side. Transfer the chicken to a platter and pour off all but 1 tablespoon of the fat in the skillet.

Return the skillet to moderate heat and add the garlic. Cook, stirring, until it starts to color, then add 2 tablespoons of the parsley and sauté briefly to release its fragrance. Add the porcini and stir briefly, then add the tomato puree, stock or diluted broth, and reserved porcini liquid. Bring to a simmer, return the chicken, skin side up, to the skillet, cover, and reduce the heat to low. Cook until the chicken is no longer pink at the bone, 20 to 25 minutes.

Transfer the chicken to a warmed serving platter. Raise the heat to high and boil the sauce until it thickens, then spoon the sauce over the chicken. Top with the remaining 1 tablespoon parsley and serve at once.