1. Remove giblets from chicken and reserve for other uses. Pull off and discard lumps of fat. Rinse bird well inside and out; pat dry. If desired, fold wing tips under first joint. Set bird breast up on a V-shaped rack in an 11- by 17-inch pan.
2. Grate 2 tablespoons peel from oranges. Cut oranges in half crosswise and ream juice; you need at least 2/3 cup. In a small bowl, mix grated peel and thyme leaves. Starting at the neck, gently ease your fingers under chicken skin to loosen it over breast. Push 3 tablespoons orange peel-thyme mixture under skin and spread evenly over breast. Place 2 orange halves (discard remainder), 4 thyme sprigs, and 2 shallots in body cavity.
3. In a bowl, mix remaining shallots, the potatoes, and carrots with olive oil. Distribute vegetables around chicken in pan. Pour 1/3 cup orange juice over chicken. Sprinkle chicken lightly with salt and pepper.
4. Roast in a 425° regular or convection oven until vegetables are well browned and tender when pierced and a thermometer inserted through thickest part of breast to bone reaches 170°, or 180° through thickest part of thigh at joint, 1 1/4 to 1 3/4 hours. After about 30 minutes, turn vegetables with a wide spatula. If pan juices start to scorch, pour about 1/4 cup water around edge of pan and stir to scrape drippings free, mixing with vegetables.
5. Insert a carving fork into the body cavity, piercing carcass; lift bird and tilt to drain juices into pan. Set chicken on a rimmed platter. With a slotted spoon, lift vegetables from pan and arrange around chicken. Let rest in a warm place about 15 minutes.
6. Meanwhile, skim and discard fat from pan. Add sherry, broth, cream, and remaining orange peel-thyme mixture and orange juice. Stir often over high heat, scraping browned bits free, until reduced to 1 cup, 8 to 10 minutes. Add salt and pepper to taste. Pour through a fine strainer into a small pitcher or bowl.
7. Garnish platter with remaining thyme sprigs. Carve chicken and serve with vegetables and sherry-cream sauce. Add salt and pepper to taste.