Mix the dough. In a medium bowl, stir together 1 cup self-rising flour and 1 cup Greek yogurt with a fork until shaggy. Turn out onto a lightly floured surface and knead for 1 minute until smooth and slightly tacky.
Shape the bagels. Divide the dough into 4 equal pieces. Roll each into a 6-inch rope, then bring the ends together and pinch firmly to form a ring.
First egg wash. Whisk the egg with 1 tablespoon water. Brush the tops and sides of each bagel generously.
Air fry — first round. Preheat the air fryer to 350°F. Place bagels in a single layer in a greased basket or perforated liner, leaving 1 inch between each. Air fry at 350°F for 5 minutes.
Second egg wash + seasoning. Brush the bagels with egg wash again, then sprinkle generously with everything bagel seasoning.
Finish air frying. Return to the air fryer at 350°F for an additional 5–7 minutes, until deep golden brown.
Cool before slicing. Transfer to a wire rack and cool for at least 10 minutes before slicing. Serve with cream cheese, butter, or your favorite topping