Preheat the air fryer to 350°F. In a large bowl, stir the flour, raisins, brown sugar, cinnamon, and salt together. Add the Greek yogurt and vanilla and stir the mixture until a loose dough forms.
Turn the dough out onto a floured clean surface and knead it until it forms a ball. Divide the dough into four sections and roll each section into balls.
Working with one dough ball at a time, roll it into a log about 8-9 inches long. Pinch the ends together to form a circle, then repeat with the remaining dough. This will make four bagels.
In a small bowl, whisk the egg and water together.
Spray the basket of the air fryer with olive oil spray and lay the bagels in the basket. Make sure they don’t touch each other, you might need to cook in batches.
Brush the egg wash all over the tops of the bagels. Cook for 8-10 minutes until the bagels are golden brown on top.