An appliance for cooking food including an upper heating plate and a lower heating plate provided with surfaces facing each other. The upper plate being movable between a closed position in which the upper and the lower plates are in contact with each other and an open position in which the upper and the lower heating plates are spaced apart. The appliance further includes parallelogram linkage constrained to the upper plate and to the lower plate to allow the upper plate to be lifted from or to approach in a parallel manner the lower plate. The appliance further includes one or more cavities for housing food to be cooked at least at one of said surfaces and at least one vent channel to put one or more cavities in fluid communication with an environment external to the appliance when plates are in the closed position.