Preheat oven to 400 degrees F. Wrap garlic heads in foil and place on small rimmed baking pan. Transfer to oven and cook 1 hour or until garlic is dark golden brown and very soft. Remove from oven and let stand for 5 minutes or until cool enough to touch. Squeeze garlic cloves from their skin into a small bowl.
Preheat grill for two-zone grilling: half of grill should be set to medium-high; other half should be off (indirect heat).
Stretch and shape dough into 14-inch circle and place on pizza pan or large tray. Brush one side of dough with 1 tablespoon oil. Use hands to transfer dough to direct heat side of grill, oiled side down. Do not worry if dough becomes a little misshapen during the transfer. Cook 2 minutes, or until the dough releases itself from the grates (do not disturb dough before it releases).
Brush top side of dough with remaining 1 tablespoon oil, then use tongs to flip dough. Cook 2 minutes or until dough releases from grates. Continue cooking dough 3 to 4 minutes longer or until dough is firm and grill-marked in all areas, flipping and rotating frequently but keeping grill closed when not flipping.
Remove dough from grill and spread with sauce. Top with chicken, cheese, everything bagel seasoning and roasted garlic cloves.
Transfer pizza back to grill on indirect heat side. Close grill and cook 8 to 10 minutes or until toppings are warmed through and crust is fully cooked.
Remove pizza from grill and top with spinach. Cut and serve immediately.
