Brine the Turkey: In a large stockpot, combine water, kosher salt, and sugar. Bring to a boil, stirring until dissolved. Let cool completely. Submerge the turkey in the brine and refrigerate for 12-24 hours.
Prepare the Turkey: Remove the turkey from the brine and rinse thoroughly. Pat the turkey completely dry with paper towels. Preheat oven to 325°F (160°C).
Season the Turkey: In a bowl, combine softened butter with chopped herbs, salt, and pepper. Gently loosen the skin over the turkey breast and rub half of the herb butter underneath. Rub the remaining butter all over the outside of the turkey.
Prepare the Pan: Roughly chop the onion, celery, and carrots and spread them in the bottom of the roasting pan. Place the turkey on the rack in the pan.
Add Liquid: Pour chicken broth or stock into the bottom of the roasting pan. Add the lemon halves to the cavity of the turkey.
Roast the Turkey: Cover the turkey loosely with foil and roast for 3 hours.
Baste and Adjust: Remove the foil and baste the turkey with the pan juices. Continue roasting, basting every 30 minutes, until a meat thermometer inserted into the thickest part of the thigh registers 165°F (74°C).
Rest: Remove the turkey from the oven, tent loosely with foil, and let rest for 20-30 minutes before carving.
Carve and Serve: Carve the turkey and serve immediately.