Preheat the oven to 375°F. Wipe the mushrooms clean with a damp paper towel, twist out the stems, and chop the stems finely.
Heat the olive oil in a large skillet over medium heat. Add the sausage and onion and cook, breaking up the sausage, until browned, about 5 minutes. Stir in the garlic and chopped mushroom stems and cook 3-4 minutes more, until the liquid has evaporated.
Take the skillet off the heat. Stir in the cream cheese, panko, half of the Parmesan, the parsley, pepper and salt until evenly mixed.
Lightly oil a rimmed baking sheet. Fill each mushroom cap with about a tablespoon of the sausage mixture (a little more for larger caps) and set it on the sheet. Sprinkle the remaining Parmesan over the tops.
Bake 18-20 minutes, until the mushrooms are tender and the tops are golden. For a deeper color, broil 1-2 minutes at the end and watch closely.
Let the mushrooms cool 5 minutes, garnish with parsley, and serve warm. To make ahead, bake and cool them, refrigerate up to 2 days, then reheat at 350°F for 10-12 minutes.