Preheat oven to 375ºF. Line a rimmed baking sheet with parchment paper and set aside. Heat olive oil in a skillet over medium heat. Add spinach and cook, until wilted, about 1 minute. Remove from heat and add artichoke hearts.
Combine cream cheese, sour cream, spinach mixture, half the Parmesan cheese, garlic, red pepper flakes and salt in a large bowl, and mix well until combined.
Using two spoons, stuff each mushroom with about one heaping tablespoon of filling mixture. Place onto prepared baking sheet and sprinkle with remaining Parmesan.
Bake until warmed through and cheese is golden-brown, about 15 minutes. Serve warm.