Preheat the air fryer: Set it to 360°F (182°C). This gives you even toasting and helps the cheese melt smoothly.
Toast the bagel: Split the bagel and place both halves cut-side up in the basket. Air fry for 3–4 minutes until lightly crisp.
Remove and set aside.
Prepare the egg: Crack the egg into a small bowl. Add a pinch of salt, pepper, and the milk or water if using. Whisk with a fork until well combined and slightly frothy.
Cook the egg: Heat a small nonstick skillet over medium heat.
Add butter or oil. Pour in the egg and gently scramble, pushing from the edges inward to form soft curds. Cook 60–90 seconds, just until set but still tender.
Remove from heat.
Melt the cheese: Place one slice of cheese on each toasted bagel half. Return to the air fryer and cook 1–2 minutes at 320°F (160°C) until the cheese is melted and bubbly at the edges. Keep an eye on it to prevent over-browning.
Add protein (optional): If using pre-cooked bacon or ham, warm it in the air fryer for 1–2 minutes.
For a pre-cooked sausage patty, 2–3 minutes usually does the trick. You want it hot and slightly crisp on the edges.
Assemble: Pile the soft scrambled egg onto the bottom bagel half. Layer on bacon, sausage, or ham, if using.
Top with tomato slices or greens if you like. Add a dash of hot sauce or a pinch of red pepper flakes.
Finish and serve: Place the top bagel half over the filling and press gently. For an extra-toasty exterior, return the whole sandwich to the air fryer for 1 minute at 320°F (160°C).
Serve immediately.