Preheat oven to 400°F (200°C). Line a baking sheet with parchment. Clean mushrooms with a damp towel, remove stems, and scrape any membrane from the caps. Toss caps in olive oil, season with salt and pepper, and place cap-side down on the sheet. Roast for 8 minutes to draw out moisture.
Finely chop reserved stems. Melt butter in a skillet over medium heat. Cook shallot for 2 minutes, then add stems and garlic. Cook for 4 to 5 minutes until completely dry and fragrant. Season and cool.
Beat softened cream cheese until smooth. Mix in Parmesan, mozzarella, cheddar, garlic, parsley, chives, Italian seasoning, onion powder, paprika, salt, pepper, and red pepper flakes. Fold in cooled cooked stems. Taste and adjust seasoning boldly.
Remove pre-roasted caps from oven, flip cavity-side up, and pat dry inside with a paper towel. Fill each cap generously with the cream cheese mixture, mounding slightly above the rim.
Mix mozzarella and Parmesan for the topping and sprinkle over each cap. Add panko if using.
Bake for 10 to 12 minutes until cheese is melted, bubbling, and golden. Broil for 1 to 2 minutes for a deeper golden top if desired.
Rest 3 minutes. Garnish with fresh parsley and serve immediately.