Whisk pumpkin puree, sugar, walnuts, pumpkin pie spice, cinnamon, and vanilla together in a bowl until well blended.
Place each of the 2 pie crusts on a lightly-floured surface, and roll out the dough thinly with a rolling pin. Using a 2 1/4-inch round biscuit or cookie cutter, cut each pie crust into 20 circles for a total of 40 circles.
Fill 20 circles with about 1 teaspoon of the pumpkin filling, leaving 1/3 inch open around the edges. Do not overfill.
Dip your finger in water and run it around the edge of each circle. Place a second pie crust circle on top. Press down the edges and crimp with a fork to seal. Whisk egg and water together in a small bowl. Brush the tops of the cookies with the egg mixture and sprinkle lightly with cinnamon sugar.
Preheat the air fryer to 360 degrees F (180 degrees C).
Place a batch of the cookies in the air fryer basket, leaving space around each for air circulation.
Bake until golden brown, about 7 minutes, and remove to a rack to completely cool. Depending on the type and size of your air fryer, you may have to cook in batches, and your timing may vary, so keep your eye on them.
Whisk 1/4 cup confectioners sugar, 1/2 tablespoon maple syrup, and milk together in a bowl to a drizzle consistency. If glaze is too thick, add a bit more maple syrup. If too runny, just add a little more confectioners' sugar. Drizzle the glaze over the cooled cookies, and allow the glaze to set before serving, about 30 minutes.