Mushroom Caps with Bone Marrow

As far as I know, this recipe is an original of Stars, and comes of my love of grilled mushrooms and marrow on toast. The cheese could be Fontina or Gruyère, but I like the aged dry Jack as made by the Vella cheese company in Sonoma. The mushrooms could be shiitake, field, or large domestic mushrooms, or even fresh cèpes or porcini. This first course is very rich.