Preheat the oven to 350 degrees F.
Remove the stems from the mushrooms and chop the stems finely. Set aside.
Place the hollow mushroom caps in a shallow bowl and toss with 3 tablespoons of the olive oil and Marsala. Set aside.
Heat the remaining 2 tablespoons olive oil in a medium skillet over medium heat. Add the sausage, crumbling it with the back of a wooden spoon. Cook the sausage for 8 to 10 minutes, stirring frequently, until it's completely browned.
Add the chopped mushroom stems and cook for 3 more minutes. Stir in the scallions and garlic and cook for another 2 to 3 minutes, stirring occasionally. Add the panko crumbs, stirring to combine evenly with all the other ingredients. Finally, add cream cheese and continue cooking until the cheese has melted and made the sausage mixture creamy. Turn off the heat, stir in the Parmesan, parsley, and season with salt and pepper, to taste.
Fill each mushroom generously with the sausage mixture. Arrange the mushrooms in a baking dish large enough to hold all the mushrooms in a snug single layer. Bake for 25 to 30 minutes, until the stuffing is browned and crusty.