Start brining the turkey 24 hours before you plan to start smoking it. Make sure that your cooler is clean and dry, and that your drain plug is inserted properly. Or clear space in your refrigerator if you plan on brining in the fridge. Spatchcock the thawed turkey.
In a large pot, add 4 cups water, 1½ cup kosher salt, ¾ cup sugar, 1 tablespoon black peppercorns, 3 bay leaves, and the fresh rosemary and thyme. Bring to a boil to dissolve the salt and sugar. Remove from the heat and add 6 cups orange juice and 8 cups cold water. Allow the brine liquid to cool completely.
Place the spatchcocked turkey breast-side down in a brine bag in the bottom of a cooler. Pour in the cooled orange juice brine, and work it around so that the turkey is completely covered. Add ice around the brine bag - if cooler brining. Close the lid of the cooler and brine turkey for a full 24 hours. Or, place the brine bag inside a large pot or roasting pan and brine in the refrigerator for 24 hours.
Preheat pellet grill or smoker to 225℉ with your choice of wood pellets. While grill is heating, prepare the turkey. Remove the turkey from the brine and pat dry with paper towels. Place on a wire cooling rack on top of a sheet tray. Season all sides liberally with Shake That All Purpose Seasoning. Then season with a lighter layer of black pepper.
Make the herbed basting butter by mixing melted butter, orange zest, chopped rosemary and thyme, and black pepper in a small bowl. Set aside.
Smoke the turkey on the grill at 225℉ for one hour. After one hour, use a basting brush to baste the turkey with the herbed butter. Then adjust the grill temperature up to 325°F and continue to cook the turkey, basting every 25-30 minutes with the melted butter. Reserve about 2 tablespoons of the herbed butter for the next step.
When the internal temperature of the turkey breast reaches about 155℉, add the small bit of remaining herbed butter to a small saucepan with the orange marmalade. Heat briefly, and then use the orange glaze mixture to baste the turkey.
Continue to cook the turkey, basting with the orange glaze every 15-20 minutes, until the internal temp of the thickest part of the breasts reaches 162℉. This allows for a few degrees of carryover cooking. (USDA recommends cooking to 165℉.)
Remove turkey from the smoker and transfer to a serving platter or cutting board. Allow turkey to rest for 30-45 minutes before carving.