Preheat Air Fryer at 350°F (177°C). Set at 15 minutes.
Slice each sweet roll in half and transfer the base to a parchment-lined Air Fryer tray on a baking tray. Then add 2 slices of Havarti cheese.
Cut the boneless turkey roast into 6 portions and place on top of the Havarti cheese.
Spread whole cranberry sauce evenly on top of the portioned turkey roast. Add the slices of brie and emmentaler cheeses to cover all sections of the 6 rolls. Then top with the remaining Havarti cheese. Lastly, cover with the top layer of the sweet rolls.
Spread softened butter on top and all the sides of the sweet rolls. Then sprinkle everything bagel seasoning and half of the fresh chopped parsley. Cover with foil, securing all the sides without touching the sliders.
Slowly insert the Air Fryer tray with cranberry turkey sliders into the lower cooking chamber, above the drip tray.
If the Air Fryer uses a basket, place the cranberry turkey sliders covered with foil onto the crisper plate and basket.
Air Fry the cranberry turkey sliders for 15 minutes or until the cheeses are melted according to preference.
For slightly crisp sweet rolls on top, Air Fry uncovered at the last 1 minute.
For crisp, golden brown cranberry turkey sliders, remove the foil and Air Fry for the remaining 3 to 5 minutes.
Transfer the leftover cranberry turkey sliders with the parchment paper onto a serving plate or a wooden board and garnish with the remaining fresh parsley.