Prepare the mushrooms: Gently twist the stems to remove them from the mushroom caps. Place the caps in a large bowl. Finely chop the mushroom stems and set aside.
Toss the mushroom caps with 1 tablespoon of olive oil until they are lightly and evenly coated. This will help them become tender while air frying. Set them aside on a plate.
In a small skillet over medium heat, add the remaining 1 tablespoon of olive oil. Add the finely chopped mushroom stems, diced onion, and minced garlic. Sauté for 5-7 minutes, until the vegetables have softened and any liquid released by the mushrooms has evaporated. Remove from heat and let cool for a few minutes.
In a medium mixing bowl, combine the softened cream cheese, parmesan cheese, mozzarella cheese, sautéed vegetable mixture, parsley, thyme, paprika, black pepper, and salt. Mix vigorously until all ingredients are fully incorporated into a uniform filling.
Preheat your air fryer to 370°F (188°C) for 3 minutes. While it preheats, stuff the mushroom caps: Use a small spoon to generously fill each cap with the cheese mixture, slightly overfilling them and mounding the filling on top.
Lightly spray or brush the air fryer basket with oil. Arrange the stuffed mushrooms in the basket in a single layer, ensuring they are not touching. You will likely need to cook in batches.
Air fry at 370°F (188°C) for 10-12 minutes, or until the mushroom caps are tender and the cheesy filling is golden brown and bubbly on top.
Carefully remove the mushrooms from the air fryer. Let them cool for 2-3 minutes before serving, as the filling will be very hot. Garnish with additional chopped parsley and serve immediately.