Combine the mashed potatoes, Gruyère cheese, Parmesan cheese, flour, and herbs. Mix well, taste for seasoning, and add salt and pepper as needed. Add the beaten egg and mix until well blended.
Shape the mashed potato mixture into balls and arrange them on a baking sheet or plate.
Set up a breading station with 2/3 cup of flour in one bowl, 2 beaten eggs in a second bowl, and the panko crumbs in the third bowl. Dip a mashed potato ball in the flour, then in the eggs. Let the egg mixture drip off and coat it with the panko crumbs. Place it back on the baking sheet or plate and repeat with the remaining balls. You should have about 18 to 20 croquettes.
Spray the air fryer basket with cooking spray, such as ghee or olive oil. Arrange 9 or 10 of the croquettes in the air fryer and spray lightly with the cooking spray.
Air fry at 350 F for 14 to 17 minutes, gently shaking the basket or turning them occasionally to ensure even browning. When done, the croquettes will be crispy and golden brown and should register at least 165 F on an instant-read thermometer inserted into the center. Remove the air-fried croquettes to a warm plate and cook the remaining croquettes.
Serve as a side dish with a garnish of parsley. Or serve the mashed potato croquettes and a snack with your favorite dip. Enjoy!