A grill accessory creates a steaming chamber on a grill that has a heat source and a rack of spaced-apart bars over the heat source. The grill accessory includes a cover configured that covers a food item and forms a steaming region below the cover. The cover operates in connection with a vapor generator that receives and holds fluid beneath the cover. The vapor generator has at least one vent opening to release steam into the steaming chamber. The grill accessory is configured so that it can rest upon the grill rack of spaced-apart bars, and so that the vapor generator transmits heat to the fluid in the vapor generator to convert the fluid to steam. The vapor generator releases the steam through the vent opening(s) into the steaming region below the cover. The steam can help melt toppings and/or introduce moisture into food items cooked on the grill.
