Dry out the cubed bread by spreading it out on a large sheet pan at room temperature for 6-8 hours (flipping them over at the halfway point). Or, air fry them at 300F for 3-4 minutes, tossing them around once to ensure even drying.
Melt the butter in a skillet over medium heat. Add the mushrooms, celery, onion, garlic and herbs. Cook until everything is softened, about 3-5 minutes.
In a large measuring cup, whisk together the broth, egg, salt and pepper.
In a large bowl, add the dried bread cubes and mushroom mixture. Toss to combine.
Gradually pour the egg mixture over the bread mixture, tossing until everything is well coated. The bread cubes should absorb most of the liquid but shouldn't be soggy.
Transfer the stuffing mixture to a greased 7-inch round baking pan (or a pan that will fit your air fryer).
Cover with foil and place in the air fryer basket. Air fry at 360F for 15 minutes.
Carefully remove the foil and air fry for another 8-10 minutes, or until the top is golden brown and crispy.
Let cool for 5 minutes before serving. (I like to transfer the stuffing to a serving dish, but it's not absolutely necessary).
Notes
Make sure your bread cubes are dried out. In my experience, day old bread isn't stale enough. I use bread that's a few days old before cutting into cubes and drying them out.
Cook veggies first. I know this is an air fryer recipe, and it would be great to avoid the stove, but the aromatics really need to be cooked first before adding them to the stuffing.
Add more broth. There should be plenty of the egg/broth mixture to coat the bread cubes. But, if they still seem dry, you can just add a bit more broth.
Cover with foil. This is necessary to prevent the stuffing from drying out in the air fryer and the top from browning too much.
Size of pan. I have a 5.8 quart basket-style air fryer and a 7-inch round pan fit best in my air fryer. You'll need to use a pan that fits your specific air fryer. If your pan is smaller, your stuffing will be thicker, so it may need a few extra minutes of air frying time.