For the brine: In a medium saucepan, bring to a boil all ingredients except the turkey. Simmer until sugar and salt are dissolved. Let cool completely. Double a one gallon re-sealable bag and fill with brine. Add turkey, seal bags and place in a shallow pan in the refrigerator for 5 to 7 days. (Just in case of leaking, check occasionally.) Remove breast from brine and rinse and dry well.
For the rub: Pulse all the ingredients in a spice grinder or food processor until it becomes a coarse paste. Rub mixture all over turkey breast. Wrap tightly in plastic wrap and refrigerate resting in a bowl for 24 hours.
To cook: Soak the chips submerged in water for 15 minutes. Place oven rack to position 4 inches below broiler. Preheat broiler on high. Drain chips and place in a 2 pound aluminum loaf pan. Broil the chips for 5 minutes, stir broil another 2 minutes. Remove to lower third of oven. Preheat oven to 250 degrees F. Place turkey skin side up in a pan fitted with a roasting rack. Place oven rack used to broil the chips in to the center of oven and roast turkey above smoking chips for one hour.
Increase the heat to 325 degrees F if convection, 350 degrees F if standard oven. Carefully turn over and continue to roast until internal temperature reaches 160 degrees F, another 1 hour 20 minutes.
Remove turkey from oven. Cover loosely with foil and cool.
To make the sandwich: Slice pastrami very thin. Toast bread. Spread mayonnaise on 1 piece, layer pastrami, onions, tomato and lettuce on top. Spread mustard on the other piece of toast. Place on top and cut it in half diagonally. Repeat with remaining ingredients.