2. Make the glaze: Stir together in a medium bowl the reduced apple cider, cider vinegar, soy sauce, ground chile, brown sugar, and garlic. Spoon about 2 teaspoons of the sauce over each hen.
3. Slip the pan into the oven and reduce the heat to 325°F. Roast the hens for 30 minutes, basting with their pan juices once or twice. Then raise the heat to 400°F., baste each hen with about 2 tablespoons of sauce, and continue roasting and basting with pan juices for 20 more minutes, or until the thickest part of the breast reads 160°F on an instant-read thermometer. At this point spoon a bit more sauce over the hens and run them under the broiler briefly, so they turn a rich, deep brown. Watch them carefully so they don't burn.
4. Remove the pan from the oven, transfer the hens to a platter, and let them rest in a warm place for 10 to 15 minutes. Roast the cornbread cubes as directed in the recipe and reheat the roasted vegetables.
5. As they heat up, set the hens' roasting pan on two burners and remove the onions from the pan. Add any remaining basting sauce to the roasting pan. Raise the heat to medium-high or high. With a wood spatula, scrape any brown glaze from the pan and stir as you boil the pan sauce for 3 minutes, or until it's rich tasting and almost syrupy. Taste for seasoning, add any necessary salt and pepper, and keep hot.
6. To serve the hens, warm a large serving platter in the oven for a few minutes. Then heap the vegetables and cornbread on it and tuck in the hens. Scrape all the pan juices over the birds and vegetables, scatter with the pine nuts if you're using them, and serve the dish hot.
From The Splendid Table's® How to Eat Weekends: New Recipes, Stories & Opinions from Public Radio's Award-Winning Food Show by Lynne Rossetto Kasper and Sally Swift (Clarkson Potter Publishers, 2011). Copyright © 2011 by American Public Media. Photographs copyright © 2011 by Ellen Silverman. All rights reserved.
In Pasta by Hand, Jenn Louis defines dumplings as "handcrafted nubs of dough that are poached, simmered, baked or sauteed." Louis, chef at Lincoln Restaurant in Portland, Oregon, says Italy's dumplings vary by region.