Preheat the oven to 375°F.
In a mixing bowl, combine the cream cheese, mozzarella cheese, Parmesan cheese, minced garlic, parsley, salt, black pepper, and red pepper flakes. Mix until well combined.
Drizzle the olive oil over the mushroom caps and toss to coat.
Stuff each mushroom cap generously with the cheese mixture, pressing it in gently.
Place the stuffed mushrooms on a baking sheet lined with parchment paper.
Bake in the preheated oven for 20-25 minutes, or until the mushrooms are tender and the cheese is bubbly and golden.
Remove from the oven and let cool for a few minutes before serving.