I've never been a huge fan of turkey - but since I started grilling it about 10 yrs ago - I'm Lovin It.
My bro in law is a long haul trucker. He brought back about 100lbs of turkey breast on Saturday because of broken seal on a few bags. His dispatcher said "get rid of them".
I inherited 4 bags of whole split breast
Anyway - I do all this on a Weber (any grille that is dome shaped).1st soak some Hickory chips and set aside.
I fire up the coals on 2 edges of grille,keeping center open for indirect cooking method. I brush the breast with conola oil,rub in kosher salt,pepper,garlic powder and last, some smoke mesquite grille seasoning.
Back on the Topic Question;
Lay the breast in center of grille and cook each side for 15 mins and continue to turn every 10 minutes or so. The last 20 minutes I throw the smoke chips on coals. Cooking takes approx 1hr +-. I cook it to 160 -165 degrees max. They will tell you 170+ deg but never tell you it continues to cook for 15 minutes+- after you remove from grille/oven (dryed out white meat[X(]
As a bonus - after the turkey was done I threw on a big ole Venison steak.
I'm drooling on the key board just talkin about it[8D]
I do the same thing with whole 12-15 lb turkey for T Day or Xmas dinner every year. For whole turkey I put a tin foil pan of seasoned water under the grate and place turkey on a roasting rack.
It might sound like a lengthy process - but you'll never cook another turkey in an oven!