Preheat the oven to 375°F (190°C). Line a baking sheet with parchment paper or lightly grease it.
Wipe the mushrooms clean with a damp paper towel. Remove the stems and finely chop them.
Heat olive oil in a pan over medium heat. Add the chopped mushroom stems and garlic. Sauté for about 3 minutes until softened. Remove from heat and let cool slightly.
In a bowl, combine the sautéed mushroom stems, cream cheese, Parmesan, mozzarella, breadcrumbs, parsley, salt, black pepper, and red pepper flakes (if using). Stir until well blended.
Spoon the filling into each mushroom cap, packing it in slightly. Arrange them on the prepared baking sheet.
Bake for 18-20 minutes, or until the tops are golden brown and the mushrooms are tender.
Garnish with extra chopped parsley and serve warm.