A whole turkey breast is easy to cook. There's no difference really between cooking a turkey breast and a chicken breast, except for size. The turkey takes a bit longer.
For best flavor we're using a wet brine this time. It should be a 4% solution, and with the assumption that 6.6 lbs turkey contains roughly 2 litres of water (70%) plus 2 litres of water for the brine that gives me 5.6 oz salt and 1.1 oz sugar (4% of 4 litres, or 4000 grams). Read more about wet brines here.
Wet brine
Add the water, salt and sugar to a pan and bring it to a boil. Remove from the stove and let it cool off completely.
Now add the turkey to the brine and leave to soak overnight.
Cooking
Remove the turkey from the brine and pat dry with a paper towel. Apply the rub evenly all over.
Fire up the grill/smoker and have it running at 140-150° C / 280-300° F. We're cooking at slightly higher temps to make sure the skin is crispy. If cooked at lower temps it tends to get rubbery. If using a grill, make sure to place the meat on the indirect side.
Place the turkey in the grill/smoker and cook it until done, i.e. when the internal temp is 65° C / 149° F. Bring the turkey breast in and let it rest on a cutting board for 30 minutes. Wrap it snugly with aluminum foil and a thick folded towel so it doesn't cool off. By doing so the carryover heat will bring the internal temp up towards 70° C / 158° F.
Slice the turkey breast in thin slices and serve it with a tasty Alabama White Sauce.