Remove any excess gobbets of fat from the turkey breast. In a large stockpot or other food-safe container, combine the water, kosher salt, and brown sugar, and stir until the salt and sugar crystals dissolve.
Add the turkey to the brine and refrigerate 6 to 8 hours or overnight. If necessary, weight with a bag of ice to keep the turkey submerged.
Drain and pat dry with paper towels; discard the brine. Put the turkey breast on a roasting rack in a shallow roasting pan. Add 1 cup of water to the bottom of the pan.
In the meantime, make the herb butter: In a microwave-safe mixing bowl, combine the butter, chopped herbs, garlic, lemon juice, lemon zest, and salt and pepper.
When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Set the temperature to 325F and preheat, lid closed, for 10 to 15 minutes.
Gently work your fingers or the handle of a wooden spoon under the skin on the breast to loosen it from the meat. Insert 2 tablespoons of herb butter under the skin on each side of the breastbone, massaging it with your fingers to distribute it evenly and push out any pockets of air.
Melt the remaining 4 tablespoons of herb butter in the microwave using medium-low heat. Brush the outside of the turkey breast with some of the melted butter.
Roast the turkey for 2 to 2-1/2 hours, or until the turkey is golden brown and the internal temperature in the thickest part of the thigh is 165F. (Use an instant-read meat thermometer.) Baste with the remaining butter after 1-1/2 hours.
Let the turkey breast rest for 15 minutes before carving. Garnish, if desired, with sprigs of fresh herbs.