Strain the pumpkin puree through a fine mesh strainer or a piece of cheesecloth for 5 minutes or until it's about the same texture as Greek yogurt.
In a marge mixing bowl, combine the flour, baking powder, and salt.
Mix in the pumpkin puree, Greek yogurt, and pumpkin pie spice (if using) to form a sticky dough.
Turn dough onto a floured surface and knead 5-6 times, until smooth.
Divide the bagel dough into 4 pieces. Roll each piece of dough into an 8-inch rope. Bring the ends of each rope together and pinch to seal.
In a small bowl, whisk egg and water together. Brush the top of each bagel with the egg mixture.
Place the bagels in your air fryer basket in a single layer. Air fry at 325ºF for 14 minutes, until criso and golden brown.