Line the air fryer basket with foil to create a well that is large enough to contain the ham. This will help contain the juices.
In a small bowl, mix together the remaining ingredients. Spread half of the garlic herb butter over the ham, and put aside the remaining half for later.
Put the ham into the foil "basket" and cover the ham with foil, preferably so that that foil is not touching the ham, and cook at 300 °F (150 °C) for 50 minutes.
Using pot holders, carefully remove the foil that's covering the ham and rub the remaining butter on top of the ham. It's fine if it melts.
Cook the ham at 375 °F (190 °C) for another 10 minutes.
Serve warm. Refrigerate any cooled, leftover ham in an airtight container for up to three days.