While the stones are heating prepare the herb butter: Mix the butter with the cheese and herbs; season it with salt and pepper. Refrigerate until ready to use.
Place a thick layer of seaweed on the grate. Place a layer of potatoes on the rack and cover them with a thin layer of seaweed. Put the corn on next and then another thin layer of seaweed. Now put on the kielbasa and top it with a thin layer of seaweed. Next mound the clams on top and cover with a thick layer of seaweed. Cover the entire bake with burlap or a tarp soaked in sea water. Keep the tarp wet by pouring sea water over the top if needed. Cook until the clams open and the potatoes are tender, about 1 hour.
Pull the husks back from the corn and remove the silk. Brush generously with the herb butter and garnish with grated Parmesan.