Important Note: For best results, completely thawed turkey must brine for at least 24 hours. Please make preparations to allow proper amount of time for brining.
In a small saucepan over medium heat, add brown sugar, salt, and 2 cups waters. Bring to boil and only cook until sugar and salt are dissolved (about 1 minute after bringing to boil). Remove from heat.
Place turkey into a large 4 to 5 gallon container or brining bag (I have a very large mixing bowl where I can fit both my turkey and brine) and add remaining water and brown sugar/salt mixture. Make sure the entire turkey is submerged by the liquid. Cover and refrigerate for at least 24 hours.
Remove turkey from brine and pat dry. Carefully separating the skin from the turkey, spread the butter under the skin on the turkey breast. Continue spreading butter on all places you can get under the skin. Season turkey with salt and pepper. Place turkey in roaster pan and stuff the cavity with the onion OR with options suggested in the above post.
Meanwhile, turn your wood pellet grill (I own a Traeger) to the Smoke setting and open lid to establish fire.
Leave grill on Smoke and place turkey in roasting pan on the grill and smoke for 2 1/2 to 3 hours.
Increase grill setting to 350 degrees and cook for additional 3 1/2 to 4 hours, or until the breast internal temperature reaches 160 degrees F.
Remove from grill and let rest for 15 minutes before slicing. Enjoy!