To make the marinade, whisk together all ingredients except for turkey in a large bowl. Add turkey and rub the spice mixture all over to coat. Let stand covered for 1 hour at room temperature or for up to 48 hours refrigerated.
Thread the turkey onto metal BBQ skewers. Rub the grill grates with oil and preheat on medium-high heat for 5 minutes, lighting half the burners but leaving an area where the grill is unlit.
When grill is super hot, add skewers to the direct-heat cooking area.
Cook until the turkey releases easily from the grates, then flip and cook until nicely grill-marked on all sides.
Move skewers to unlit part of the grill, close the lid and continue cooking until internal temperature of 165ºF is reached, 8-12 minutes total cooking time.
Notes
Chicken Substitute: You may substitute 3 lbs of boneless, skinless chicken thighs or breasts for the turkey roast if you prefer. Increase to 2 1/4 kosher salt (as the turkey breast roast comes brined/seasoned).
Safety Note: Use oven mitts when flipping metal skewers as they get very hot.