Preheat the air fryer to 380°F while you prep the filling.
Twist out mushroom stems. Finely chop the stems and pat the caps dry.
Stir cream cheese, Parmesan, chopped stems, mayonnaise, parsley, garlic, lemon juice, 1/4 tsp salt, pepper, and paprika until smooth.
Toss mushroom caps with 1 tbsp olive oil and the remaining 1/4 tsp salt to season.
Combine panko with the remaining 1/2 tbsp olive oil until lightly moistened.
Fill each cap with a rounded teaspoon of the creamy mixture. Sprinkle with the oiled panko.
Arrange stuffed caps in a single layer. Air fry 8–10 minutes until tops are golden and mushrooms are tender.
If using mozzarella, add it on top and air fry 1 minute to melt.
Let rest 2 minutes. Garnish with extra parsley and serve warm.