Preheat oven to 400°. Put the mushroom caps open-side down on a sheet pan. Run the empty mushroom caps in the oven for 5 or 6 minutes. Set aside. Leave the oven on.
Meanwhile, melt 4 T. of the butter in a skillet over medium heat. Briefly sauté the scallions--about a minute. When the scallions are wilted add the minced shrimp and the garlic. Cook, stirring, for another minute or so until the shrimp is opaque.
Off the heat add ½ cup of the breadcrumbs, ⅓ cup of parmesan, sherry, cream, parsley, salt, and pepper, to the shrimp in the skillet, mixing well. Taste for seasoning and adjust if needed. Use to stuff the mushroom caps.
Melt the remaining butter, and toss with the remaining bread crumbs and parmesan. Sprinkle a little of this mixture on each stuffed mushroom. Bake for 12-14 minutes or until the crumb topping is golden brown. Serve hot.