How to Make It
In a small bowl combine all BBQ sauce ingredients. Set aside.
Leaving the root end intact, quarter the cabbage. In a large bowl toss cabbage in oil and salt. Rub to coat. Heat a large, heavy bottomed skillet on over medium high heat. Place cabbage quarters face side down and cook until charred. Turn over to opposite side and repeat. Turn over to back side and paint charred sides of cabbage with tamarind BBQ. Cook until tender but not too mushy. Remove from heat and allow to rest.
Between four plates, divide the charred cabbage. Top with cheddar, cilantro and busted up tortillas. Serve immediately.