To make the deaa, mix together the jalapeno, garlic, and lemon juice. Cover and refrigerate until ready to serve. This spicy relish should be offered on the side of the casserole, so that your guests can add spice to their taste.
Place the chicken in a Dutch oven and fill with enough water to cover; stir in the onion, 1 tablespoon of allspice, bay leaves, cardamom, rosemary, salt, and pepper.
Bring to a boil over high heat, then reduce to medium-low and simmer for 1 hour.
Preheat oven for broil.
Remove the chicken pieces from the Dutch oven and place on a baking sheet; season each piece with salt and pepper and the remaining allspice. Reserve the chicken stock.
Broil the chicken pieces on the top rack of the oven until the chicken starts to crisp and turns golden brown.
Cut the pita bread into large chunks, and arrange the pieces in layer across the bottom of a casserole dish, then spread the rice over the pita. Pour 4 cups of the reserved stock over the pita and rice, allow to stand for 5 minutes to soak in the stock. If necessary, add more stock to make the dish moist. Place the chicken on top of the rice and garnish with parsley.