Wash and slice (butterfly) zucchini and squash starting about 1 1/2 inches from the stem end slicing down to the other end. Make about 4 slices per vegetable.
Place in a container and pour teriyaki marinade to coat all slices. Cover container and refrigerate for 12 hours.
When ready to cook, fan out slices on a medium heated grill and baste with leftover marinade. Grill five minutes each side. Just before removing from grill, top with parmesian cheese (allow cheese to melt). Serve fanned out.