Place 6 large eggs in the air fryer basket in a single layer. Use a wire rack or silicone muffin cups to keep them from rolling, if needed.
Air fry at 250°F (120°C) for 16 minutes for fully cooked yolks. Do not preheat the air fryer.
While the eggs cook, fill a large bowl with ice and cold water.
As soon as the timer ends, use tongs to transfer the eggs immediately to the ice bath. Let them sit for at least 5 minutes (10 minutes is ideal).
Tap each egg on the counter, then roll under your palm to crack the shell all over. Peel under cold running water for the cleanest result.
Slice each peeled egg in half lengthwise. Pop the yolks out into a small bowl and arrange the whites cut-side up on a serving plate.
Mash the yolks with a fork until completely smooth (or press through a fine-mesh strainer for a silky texture).
Add the mayonnaise, Dijon mustard, vinegar, salt, and pepper. Stir until creamy and well combined.
Taste and adjust — add more salt, vinegar, or mustard to your preference.
Spoon the filling into the egg whites, or pipe it in for a prettier presentation.
Sprinkle with paprika and any optional garnishes. Serve immediately, or refrigerate covered for up to 24 hours before serving.