Rinse the rice in cool water, drain, and add the rice to a medium saucepan with a lid. Add 3 cups cold water and 1 teaspoon salt. Set over high heat and bring to a boil, stirring once. Immediately reduce the heat to low and cover the pot. Cook for 45 to 55 minutes, or until all the liquid has been absorbed. Place a rack in the middle of the oven and preheat the oven to 325 degrees F.
While the rice is cooking, spread the chestnuts on a baking sheet and toast them in the oven for about 10 minutes. Remove the chestnuts from the oven. In a large bowl, mix together the rice, chestnuts, onion and herbs. Set aside. Turn up the oven to 375 degrees F. Pat the Cornish hens dry with a paper towel. Remove the livers, hearts and gizzards and discard or reserve for another use. Lightly sprinkle the cavity of each hen with salt and loosely fill with the rice stuffing, leaving a little space to allow the rice to expand during roasting. Truss the birds if you like. You will have some stuffing left over. Spoon it into a small casserole with a lid and set aside or refrigerate. Rub the skin of the hens with olive oil and salt and pepper to taste and place, breast side down, on a rack set in a roasting pan. Bake for 15 minutes, then baste with the pomegranate juice. Continue basting with pomegranate juice every 15 to 20 minutes, until the hens are dark golden brown, the juices run clear when the hens are pierced at the thigh with a fork, and an instant-read thermometer inserted into the thickest part of the thigh, not touching the bone, registers 175 degrees F to 180 degrees F, 60 to 65 minutes. During the last 25 minutes of roasting time, slide the casserole of extra stuffing into the oven to heat. Remove the birds from the oven and transfer them to a platter. Cover them with foil and let rest for 10 to 15 minutes. Place the roasting pan with the juices on the stovetop over medium-low heat, add about 1/2 cup of the chicken stock, and scrape up any roasted bits from the bottom of the pan. Sift the flour into the cooking juices and whisk well. Slowly whisk in 1 1/2 cups of the remaining stock. Let simmer until the mixture is thick and smooth, 5 to 6 minutes. Season with salt and pepper to taste. To serve, place 1 hen on each plate, nap with the gravy, and garnish with the pomegranate seeds, if desired. Pass the extra stuffing at the table. OPTION: Pomegranate Balsamic Glaze: I treat this glaze like barbeque sauce, brushing it on once during the cooking and once again when I bring the hens out of the oven. Then I put the rest in a small bowl and pass it at the table as a sauce. Combine 1 cup pomegranate juice and 1 cup balsamic vinegar. Heat over medium-low heat for 15 to 20 minutes, or until the mixture is syrupy but not as thick as molasses. This makes about 1 cup glaze. The glaze keeps in the refrigerator for up to 1 month
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