Take two slices or bread and butter one side of each slice. Place one slice butter side down in the air fryer.
Top with the slices of ham and the cheese. (Tear apart the cheese if needed to fit onto the bread).
Add the other slice of bread to the sandwich, butter side up.
Cook at 360 degrees F (180 degrees C) for 6 minutes, flipping after 4 minutes if desired.
Remove and slice. Sprinkle with dried oregano if desired.
Notes
If you want to make sure both sides of your bread are super-crispy, flip after 4 minutes of cook time.
Many types of cheese work well here. I would suggest using whatever cheese you love using in a ham and cheese. I used cheddar for mine.
You can customize this by adding dijon mustard or other seasonings. If I want it spicy, I add a tiny bit of piri piri oil.
If you are using lighter bread, like sandwich bread, add something heat-safe to the top to weigh the top slice down so your sandwich stays together and the top slice doesn't fly off.