Heat your barbecue on high with all burners going and lid down. (Should get to 450-500 degrees)
Mist or rub olive oil all over the turkey breast, and season all over with salt and pepper
Once grill is hot enough, put oiled & seasoned turkey breast on the middle or, if you have a two burner grill, on one side.
Let turkey sear and turn, searing the other side so it's nice and brown all over.
Now turn the heat right under your turkey breast off, and put the lid down. If you have more than two burners, your turkey breast will be right in the middle with no heat under, but heat coming from both sides.
If you have two burners, you will need to rotate the turkey breast every 15 minutes or so to ensure even cooking. Do this quickly to keep the heat from escaping. Let the turkey breast roast on the BBQ for about 30 minutes and turn.
Meanwhile put the cranberry sauce and orange brandy or juice in a bowl and with a stick blender or electric mixer, puree until you have a nice thick glaze.
Brush turkey every 15 minutes or so with glaze, turning and brushing the other side. Turkey is finished roasting when an internal thermometer reads 170 degrees.
Brush with more glaze and let rest for 5 minutes before slicing.
To cook this recipe in the oven, preheat oven to 400° Put prepared turkey breast on a rack in center of oven, and continue as with grilling instructions.