Preheat oven to 400°F (200°C) and brush a baking sheet with olive oil. Wipe mushrooms clean, remove stems, and finely chop the stems.

In a skillet over medium heat, cook the chopped stems with 2 tbsp olive oil and ¼ tsp salt for about 4 minutes. Add garlic and cook 30 to 60 seconds until fragrant. Transfer to a bowl and cool slightly.

Stir cream cheese, Parmesan, mozzarella, pepper, and parsley into the stem mixture until evenly combined.

Mound filling into mushroom caps, press panko on top, and bake 18 to 20 minutes until golden. Broil 45 seconds for more color if needed. Let rest 3 minutes, then garnish with parsley and serve warm.