Make the béchamel by melting the unsalted butter (unsalted_butter) in a small saucepan over medium heat, whisking in all-purpose flour (flour) until a pale roux forms, then slowly whisking in whole milk (milk) until smooth and thickened; season with salt (salt), freshly ground black pepper (black_pepper) and a pinch of ground nutmeg (nutmeg) and thin with water (water) if necessary.

Spread softened unsalted butter (unsalted_butter) on one side of each slice of sliced sandwich bread (bread); on four unbuttered sides, optionally spread Dijon mustard (dijon) then a thin layer of warm béchamel (béchamel made above).

Assemble sandwiches by placing two slices of sliced cooked ham (ham) and about 1/3 cup of grated Gruyère (gruyere) on the béchamel-covered bread, then top with the remaining bread slices so buttered sides face outward.

If desired, lightly brush the exterior of each sandwich with olive oil or neutral oil (oil) and spread a thin layer of béchamel (béchamel) on top before sprinkling the extra grated cheese for topping (extra_topping_cheese) evenly over the surface.

Preheat your air fryer to 375°F (190°C). Arrange sandwiches in a single layer in the air fryer basket and cook for about 6 minutes, then flip and continue cooking for another 4 to 6 minutes until the bread is golden and cheese is melted and bubbling.

After cooking, let the sandwiches rest for 1 to 2 minutes, then sprinkle with freshly ground black pepper (black_pepper), a light dusting of paprika or cayenne (paprika) if using, and chopped chives or parsley (herb_garnish) before serving.

Optional alternative finish: if the top needs extra browning, transfer sandwiches to a preheated broiler for 1 to 2 minutes to gratinate the cheese, or use an oven at 425°F (220°C) finishing for 1–2 minutes under high heat.