Adjust oven rack to lower-middle position and heat oven to 375 degrees. Pat chicken dry with paper towels. Melt 4 tablespoons butter in small bowl in microwave, about 45 seconds. Stir in 1 tablespoon sage, 1 tablespoon thyme, 1 teaspoon salt, and ½ teaspoon pepper. Brush chicken with herb butter. Melt remaining 2 tablespoons butter in 12-inch ovensafe skillet over medium heat. Add onions, celery, ½ ­teaspoon salt, and ½ teaspoon pepper and cook until softened, about 5 minutes. Add remaining 1 tablespoon sage and remaining 1 tablespoon thyme and cook until fragrant, about 1 minute. Off heat, place chicken, breast side up, on top of vegetables. Arrange bread cubes around chicken in bottom of skillet. Transfer skillet to oven and roast until breasts register 160 degrees and thighs register 175 degrees, about 1 hour, rotating skillet halfway through roasting. Carefully transfer chicken to plate and tent loosely with aluminum foil. Holding skillet handle with potholder (handle will be hot), stir bread and vegetables to combine, cover, and let stand for 10 minutes. Add broth and any accumulated chicken juice from plate and cavity to skillet and stir to combine. Warm stuffing, uncovered, over low heat until heated through, about 3 minutes. Remove from heat, cover, and let sit while carving chicken.