A capon, which weighs a good eight or nine pounds, is a young male chicken that has been neutered. The snow-white breast meat is very tender and finely textured. You can find capons fresh or frozen at butcher shops and many supermarkets.
Let capon stand at room temperature 1 hour. Melt 2 tablespoons butter in a medium saucepan over medium-high heat. Add chopped onion, pancetta, and 1 teaspoon salt, and cook, stirring occasionally, until pancetta begins to render fat and onion is translucent, about 3 minutes.
Add 1 cup broth and the figs to pan, and bring to a boil. Remove from heat, and let stand 10 minutes.
Stir orange zest and juice, liqueur, and chopped sage into broth mixture. Tear bread into 1 1/2-inch pieces, and transfer to a large bowl. Pour broth mixture over bread, and stir until well combined. Fold in egg.
Preheat oven to 425 degrees. Place orange wedges in a single layer in the center of a roasting pan; add onion wedges, sage sprig, and capon neck. Stir together remaining tablespoon salt and the pepper, and season body cavity of capon with half the mixture. Pack body and neck cavities with stuffing. Place capon on top of orange mixture in pan. Rub remaining 2 tablespoons butter all over capon, and season with remaining salt-pepper mixture.
Roast capon 45 minutes. Reduce oven temperature to 350 degrees, and roast, basting every 15 minutes, until a thermometer inserted into the thickest part of a thigh reads 165 degrees, 55 to 65 minutes more, depending on size of capon. (If skin becomes deep golden brown before capon is fully cooked, loosely tent with foil.)
Transfer capon to a platter, and tent with foil to keep warm. Let rest at least 15 minutes before carving. Meanwhile, shred neck meat, and set aside. Discard oranges, onions, and sage in roasting pan. Tilt pan, and remove excess fat with a spoon. Whisk together 1/4 cup broth and the flour.
Place pan on 2 burners over medium-high heat. Add remaining 1 1/4 cups broth, scraping up browned bits with a wooden spoon. Bring to a boil, whisk in flour mixture, and boil 1 minute. Pour gravy through a fine sieve into a bowl, stir neck meat into gravy, and serve alongside capon and stuffing. Stuffing (without egg) can be refrigerated, covered, up to 1 day. Bring to room temperature before folding in egg and filling capon.