Plump the raisins (optional). Place raisins in a small bowl and cover with hot water. Soak 5–10 minutes, then drain and pat dry. This keeps them juicy in the air fryer.
Mix the dough. In a large bowl, combine self-rising flour, cinnamon, and brown sugar (if using). Add the Greek yogurt and vanilla extract (if using). Stir with a spatula until a shaggy dough forms.
Add the raisins. Fold the drained raisins into the dough until evenly distributed.
Knead briefly. Turn the dough out onto a lightly floured surface and knead for about 1 minute until smooth. Add a sprinkle of flour if too sticky, but avoid adding too much.
Shape the bagels. Divide the dough into 4 equal portions. Roll each portion into a ball, then poke a hole in the middle with your thumb. Gently stretch into a bagel shape, making the hole slightly larger than seems necessary.
Apply the egg wash. Whisk the egg yolk with 1 tablespoon water. Brush the tops and sides of each bagel with the egg wash. If using, sprinkle with cinnamon sugar.
Preheat the air fryer. Preheat to 350°F (175°C) for 3–5 minutes.
Air fry the bagels. Lightly spray the air fryer basket or tray with cooking spray (or line with perforated parchment paper). Place the bagels in a single layer, leaving space between them. Air fry at 350°F for 10–12 minutes, until deep golden brown.
Cool and serve. Transfer the bagels to a wire rack and let them rest for at least 5 minutes before slicing. Serve warm with cream cheese, butter, or your favorite topping.