An accessory is provided for adapting cooking grills, especially grills including a hinged lid, for improved cooking of pizzas and other foods. The accessory includes a body adapted to be disposed between the base and lid portions of the cooking grill, the body being configured to mate with an inner surface of the lid and to cooperate with the base and lid portions to define therebetween a substantially-enclosed cooking chamber when the lid is positioned in a partially-closed position between the open and closed positions. A hinged-lid grill including the accessory is provided also.