Place the potato chunks in a medium pot and cover with cold water. Bring to a boil over medium-high heat, add 3 grams of the salt, and cook for 15 to 18 minutes until the potatoes are very tender when pierced with a fork.
Drain the potatoes well and return them to the warm pot for 1 minute to let excess moisture evaporate. Mash until smooth, then stir in the butter, milk, Parmesan, parsley, the remaining 2 grams salt, black pepper, and 1 beaten egg until fully combined.
Transfer the potato mixture to a shallow dish and spread it out so it cools faster. Chill for 15 minutes, or until firm enough to shape without sticking excessively.
Set up a breading station with the flour in one shallow bowl, the remaining egg beaten in a second bowl, and the breadcrumbs in a third bowl.
Scoop the chilled potato mixture into 16 equal portions and shape each one into a short log or oval croquette. If the mixture becomes sticky, lightly dust your hands with flour.
Coat each croquette first in the flour, then in the beaten egg, and finally in the breadcrumbs, pressing gently so the coating adheres evenly on all sides.
Preheat the air fryer to 200°C for 5 minutes. Lightly spray the basket with olive oil spray and arrange the croquettes in a single layer with a little space between them. Spray the tops lightly with more olive oil spray.
Air fry the croquettes in batches for 10 minutes, turning them carefully halfway through, until they are deep golden and crisp on the outside.
Transfer the cooked croquettes to a serving platter and serve hot, with marinara or garlic aioli if desired.