Begin by creating the brine in a stockpot. Combine water, salt, and brown sugar, heating and stirring until the salt and sugar completely dissolve.
Add aromatics including garlic, bay leaves, peppercorns, herbs, and lemon. Allow the brine to cool completely before proceeding.
Place the turkey breast in a brining bag or container, then carefully pour the cooled brine over the meat, ensuring it is fully submerged. Refrigerate the turkey in the brine for 12 to 24 hours, taking care not to exceed this time frame.
Remove the turkey from the brine and rinse it thoroughly under cold water. Pat the turkey breast completely dry with paper towels. Create a seasoning mixture by combining olive oil with dried herbs and spices.
Massage this seasoning all over the turkey breast, making sure to get beneath the skin. Let the seasoned turkey sit at room temperature for 30 minutes before grilling.
Prepare your grill for two-zone cooking, aiming for a temperature between 325 and 350 degrees Fahrenheit. Place the turkey breast skin-side up on the cooler side of the grill. Cook for approximately 15-20 minutes per pound, using a meat thermometer to monitor the internal temperature.
The turkey is done when it reaches 165 degrees Fahrenheit at its thickest point.
Once the turkey reaches the proper internal temperature, remove it from the grill and tent it loosely with aluminum foil. s
Allow the meat to rest for 15-20 minutes, which helps redistribute the juices and ensures a moist and tender result. Slice the turkey breast against the grain and serve with your favorite sides.