Cut the mushrooms into large bite-size pieces. Note: these pieces will shrink after cooking.
Heat a non-stick skillet with a tablespoon of oil over medium heat. Sauté mushrooms for 2-3 minutes or until they release their aroma. Season with a pinch of salt and continue to cook for another 3 minutes or so until a brown crust forms. Set aside to cool while you prepare the rice paper.
Setup up the wrapping station. Fill a shallow plate with water, prepare a chopping board, and lightly grease a large plate. Cut the rice paper in half and soak it in the water. Count to 20. Remove and place them on the chopping board. If the paper seems hard, let it stay on the chopping board for another few seconds. The moist from the water will slowly soften the paper.
Place a piece of mushroom on top and wrap it into a nugget, sealing the sides as you go. Use two pieces of mushrooms if you have smaller cuts. Transfer the nuggets to the greased plate. Repeat with the remaining ingredients.
Preheat the air fryer to 390F for 3 minutes. Spray/brush the inner rack with a thin layer of cooking oil. Arrange the nuggets in one layer in the rack then spray/brush the top with oil. Air fry for 5-6 minutes, with a shake in between until the skin turns white and crispy. Air fry in batches if you have a small machine.
While waiting for the last batch to finish, whisk together the sauce in a bowl.
When ready, using the same non-stick skillet you cook the mushrooms with, pour in the sauce and set to medium heat. Cook the sauce until it thickens into a glaze, stirring regularly, about 2-3 minutes. When you see large bubbles forming, that means the sauce is starting to thicken.
Add the nuggets and quickly toss them together until they are coated with sauce. Serve immediately.