Prepare turkey: Remove giblets and neck. Combine dark brown sugar and kosher salt in plastic container. Add 4 cups hot water to container; stir until sugar and salt dissolve. Add ice cubes, peppercorns, and thyme; place turkey in brine. Add cold water to cover (about 6 qt.). Weight turkey down using a cast-iron lid, if necessary. Cover and chill 48 hours.
Prepare dressing: Preheat oven to 350°. Bake hazelnuts in a single layer in a shallow pan 8 to 10 minutes or until toasted and fragrant, stirring halfway through.
Melt butter in a large Dutch oven over medium-high heat. Add onions and celery, and sauté 10 to 12 minutes or until tender. Add bread cubes and hazelnuts; stir to coat. Season with salt and pepper to taste. Let cool completely (about 1 hour).
Remove turkey from brine; discard brine. Place turkey, breast side down, on a work surface, and spoon 4 to 5 cups dressing into neck cavity, pressing firmly. Replace skin over neck cavity, and secure using wooden picks. Turn turkey over, and spoon remaining dressing into body cavity. Tie ends of legs together with string; tuck wingtips under. Pat turkey dry with paper towels. Brush turkey with 3 Tbsp. olive oil; sprinkle with 1 Tbsp. salt and 2 tsp. pepper. Place turkey, breast side down, on a rack in a large roasting pan. Pour 2 cups water into pan.
Bake at 350° for 2 to 2 1/2 hours. Turn turkey over, breast side up. Bake 2 to 2 1/2 hours or until a meat thermometer inserted into thigh registers 180° and center of dressing registers 165°, shielding with aluminum foil during last hour of baking. Let turkey stand 20 minutes before carving.
*Frozen whole turkey, thawed, may be substituted.
Note: Depending on the size of your turkey cavity, you may have leftover dressing. Stir 1/2 to 1 cup chicken broth into remaining dressing, and place in a lightly greased 11- x 7-inch baking dish. Bake at 350° for 25 to 30 minutes or until thoroughly heated.