Rinse and wipe the mushrooms clean. Remove the stems and chop them finely.
Place the mushroom caps on the lined baking sheet. Drizzle the caps with olive oil and season them to taste with salt and pepper. Broil the caps for 5 minutes.
In a large skillet, cook the bacon until crisp. Remove the bacon from the skillet and drain the bacon bits on paper toweling. Set them aside for now.
In the skillet of bacon drippings, cook the mustard greens, green onion, and chopped mushroom stems until the greens are wilted. Stir in the cooking sherry and allow to cook until almost evaporated. Add the cream and 5 1/3 tablespoons (1/3 cup) cheese. Cook for a minute or two more on low heat until the cream has started to thicken. Stir in the bacon.
Drain off the accumulated juices from the mushroom caps. Fill the caps with the mustard greens mixture. Eat any leftover filling with sourdough toast. Remember to make extra filling next time.
Place the filled caps on the baking sheet. Top the mushrooms with the bread crumbs and remaining cheese. Broil for 2 minutes until golden. Serve immediately.
Make Ahead: Assemble and refrigerate 1 to 2 days before you plan to bake and serve them.