Preheat oven to 350°F.
Wipe mushrooms clean with lightly damp paper towels. Remove stems and scoop out the brown gills from inside the mushrooms, being careful not to break through the shell.
Place the mushroom caps into a mixing bowl and cover with olive oil. Gently stir until the mushrooms are coated in the oil. Arrange mushroom caps with the opening facing up on a rimmed baking sheet lined with parchment paper.
In a large skillet over medium-high heat, cook sausage until browned, breaking it apart with your spatula into crumbles. Add 2 minced garlic cloves and 1/2 cup sauerkraut. Let cook for 1 or 2 minutes then, remove from heat. Stir in salt and pepper and 1/2 cup cream cheese along with 1/2 cup of mozzarella cheese.
Divide and stuff the sausage mixture between the mushroom caps then cover each of them with the remaining mozzarella cheese. Sprinkle them with parmesan cheese and bake uncovered in the center of the oven for 18 - 20 minutes.
Garnish with fresh Parsley