Clean cauliflower, dry, trim off greens, and set aside, careful not to break apart.
Slather the outside of the cauliflower with olive oil.
Place all dry ingredients in a medium bowl whisk until completely blended together.
Rub entire cauliflower head with dry rub getting into all the nooks and crannies.
Place cauliflower head into a greased or foil-lined pie pan.
Add a cup of broth, wine, or water to the bottom of the pan to prevent the bottom from burning.
Place cauliflower onto the grill and cook until fork-tender, 45-60 minutes.
Remove from the oven and let sit for 5 minutes. Pull or cut apart.
Serve with chimichurri sauce or pesto.
Optional: Place cauliflower into a heavy-duty foil-lined 9 x 9 pan. Add broth, wine, or water to the bottom of the pan to prevent burning. Preheat oven to 425 degrees and cauliflower in the center of the oven. Cook for 45 to 60 minutes depending upon the size of the cauliflower. Check to see if it is fork-tender and not burning. Add broth, wine, or water to the bottom of the pan to prevent burning.