Make the marinade: in a container with a lid large enough to hold the turkey breast , combine the butter, olive oil, vinegar, shallots, garlic, Worcestershire sauce, brown sugar, thyme, salt and pepper. Place the turkey in the container and turn it so that it is well coated with the mixture. Cover and marinate in the fridge for 6 to 36 hours, turning it occasionally as you are able.
Heat half of the grill to medium, and leave half at medium low, which will be the indirect heat zone. Carefully oil the grill grates. Place the turkey breast over the medium heat zone, and grill for about 5 minutes on each side (you may only be able to get the breast to lay flat on two or three sides, which is fine).
After about 15 minutes, transfer the breast to the indirect heat zone of the grill, cover, and allow to cook for anywhere from 45 minutes to 1 hour 15 minutes, depending on how large your grill is, and therefore how intense the indirect heat is. Check starting at 45 minutes with an internal thermometer, and pull the turkey from the fire when the internal temperature in the thickest part reaches 165°F. Transfer the turkey to a cutting board and let sit for 15 minutes before slicing and serving.
Arrange the sliced turkey on a platter and tuck a variety of fresh herb sprigs amidst the sliced meat for a pretty presentation.