Add butter to inner pot of Instant Pot Duo Crisp + Air Fryer. With lid off, Select Saute, then set to High Temperature. Stir in mushrooms, and 1/4 tsp each salt and pepper. Cook for 3 to 5 minutes or until mushrooms start to brown. Stir in onion, celery, carrot, rosemary, garlic, and remaining salt and pepper; cook for 2 to 3 minutes or until softened. Stir in ground beef; cook for 3 to 5 minutes or until starting to brown. Stir in tomato paste; cook for 1 minute. Press Cancel.
Stir in broth, Worcestershire sauce and mustard. Place lid on pot and lock in place to seal. Select Pressure Cook/Manual Setting on High Pressure for 4 minutes.
When pressure cooking is complete, Quick Release the pressure. Once pressure is released, remove the lid.
With lid off, select Saute setting and set to High Temperature. Whisk flour with 2 tbsp water until smooth; whisk into beef mixture. Bring to boil; cook for 2 to 3 minutes or until thickened.
Sprinkle hash browns, Cheddar and Parmesan cheese over top.
Using the Air Fryer Lid select Roast at 400°F for 25 to 35 minutes or until topping is golden brown and bubbling. Sprinkle with parsley.