A dual purpose, single use wood grill brush for cleaning a grilling surface and thereafter providing a flavor enhancing smoke. The device is a thin sheet of wood selected for the flavor enhancing characteristics of the smoke therefrom when slowly burned, which sheet is desirably soaked in water to make the wood flexible so that it may be manually used to clean the grilling surface prior to grilling, and then deposited on the heat source where it smokes rather than flames because of the absorbed water content. Exposing the food being grilled to such smoke during the grilling process provide a unique flavor to the food. One embodiment of the device includes a flat edge on one end and a plurality of longitudinally extending fingers at the other end, both useful in the cleaning process. Other embodiments of the device specifically for grilling surfaces with spaced parallel rods include a thin sheet of wood with notches for selectively cleaning the entire surface of the rods. Methods are also disclosed.