Heat your air fryer to 350°F so it reaches temperature while you prep. In a small bowl, beat the egg well until completely uniform—this ensures an even golden wash on all bagels. Combine the sesame seeds and everything bagel seasoning in a shallow dish for easy coating. Have a clean work surface ready and lightly dust it with self-rising flour.
In a medium bowl, combine the skyr, self-rising flour, 1/4 teaspoon salt, and baking powder. Stir until a shaggy dough forms, then turn it out onto your floured work surface and knead for about 1-2 minutes until smooth and cohesive. The dough should feel slightly sticky but manageable—this high-protein combination creates a tender bagel, so don't overwork it. I find that skyr's thickness is key here; thinner yogurts will make the dough too wet, which is why I always use Siggi's.
Divide the dough from Step 2 into 4 equal pieces. Flatten each piece into a disk about 1/2-inch thick, then use your thumb or finger to poke a hole in the center of each one. Gently stretch and widen the hole to create a bagel shape with a ring about 1 1/2 inches thick—this ensures even cooking throughout.
Brush each bagel generously with the beaten egg wash from Step 1, then immediately dip or sprinkle the seed mixture onto the top and sides of each bagel, pressing gently so the toppings adhere. I like to coat the top surface most heavily for a rustic, appealing look.
Place the coated bagels from Step 4 on a piece of parchment paper in the air fryer basket, spacing them so they don't touch. Air fry at 350°F for 8 minutes, then carefully flip each bagel over and air fry for another 8 minutes until golden brown on both sides.
Remove the bagels from the air fryer and let them cool on a wire rack or plate for about 5 minutes before serving. This brief rest allows them to set up slightly while still remaining warm and tender.