Parcook the potatoes: Put 16 oz potatoes into a microwavable bowl. Microwave for 7 minutes on the highest setting. Leave the potatoes covered and allow to cool for at least 5 minutes.
Shred the potatoes: Once they are cool enough to handle, shred them with the largest holes of a box grater.
Season the potatoes: In a large bowl, combine the shredded potatoes, 2 tbsp flour, 1/2 tsp onion powder, 1/2 tsp garlic powder, 1/4 tsp salt, 1/4 tsp black pepper, 1 tbsp parsley, 0.5 oz Parmesan cheese, 2 tbsps heavy cream, and 1/2 tbsp olive oil.
Shape the hash browns: Gently press in the palm of your hand into an oblong, rectangular shape.
Cook the hash browns: Preheat the air fryer for 5 minutes at 390°F. Gently place them into the air fryer and brush the remaining 1/2 tbsp olive oil on top. Cook for 10 minutes. Flip and cook for another 5 minutes on the other side.
Serve: Transfer the hash browns into a serving dish. Put 1 tbsp Heinz ketchup and 1 tbsp mayonnaise into small sauce bowls. Serve warm.