In a stockpot or large bowl, combine the boiling water, kosher salt, and curing salt, if using, and whisk until the salts dissolve, about 30 seconds. Stir in the ice water, brandy or Cognac, cinnamon sticks, and tangerine or orange zest. Let the brine cool to room temperature, about 1 hour.
Pat the turkey breast dry with paper towels. If the turkey breast is tied with string, leave it intact. Place the turkey in a jumbo resealable plastic bag. Pour in the brine, seal the bag, and place in a large bowl or roasting pan to catch any unexpected leaks. Refrigerator for at least 12 hours or as long as 24 hours, turning it several times to evenly infuse the turkey with the brine.
Remove the turkey breast from the brine, discarding the brine. Rinse the turkey and pat it dry. Place the turkey on a wire rack set inside a roasting pan and refrigerate until the surface feels dry yet tacky, 1 to 2 hours. Lightly brush the turkey breast with the olive oil.
If you’re using a grill, set up the grill for indirect grilling and preheat to 350°F (180°C). Brush and oil the grill grate. Add the wood chips to the coals. Grill the turkey over indirect heat until the outside is golden brown and the internal temperature in the thickest part of the meat reaches 165°F (75°C), 1 to 1 1/2 hours. After 30 minutes, begin basting the turkey with extra-virgin olive oil, and continue basting every 15 minutes. If you’re using a smoker, light your smoker according to the manufacturer’s instructions and preheat to 250°F (120°C). Add the wood as specified by the manufacturer. Place the bird in the smoker. Smoke until the outside is bronzed with smoke and the internal temperature of the meat reaches 165°F (75°C), 2 1/2 to 3 hours. After 1 hour, begin basting the turkey with extra-virgin olive oil and continue basting every 45 minutes.