Position rack in center of oven and preheat to 350°F. Generously grease/butter (or spray with non-stick cooking spray) a 12-cup muffin pan. Set aside.
In a large bowl, whisk together eggs, milk, salt, and pepper until scrambled. Evenly divide ham and cheese between the 12 muffin cups. Pour the egg mixture on top, until all muffin cups are evenly filled. Bake for 20 to 25 minutes or until puffed up and cooked through.
Place pan on a cooling rack and immediately run a thin, sharp knife (or a thin spatula, if you're worried about scratching your pan) around each egg "muffin" to loosen. Allow to set for a few minutes before carefully lifting eggs from the pan.
Slice open a biscuit and sandwich an egg round between the two halves. Serve immediately or allow to cool and wrap in plastic wrap. Refrigerate (if consuming in the next few days) or place in a gallon-sized freezer bag and freeze. To reheat, remove the plastic wrap, wrap in a paper towel, place on a plate, and microwave for 30 seconds to 1 minute (if refrigerated) and 1 to 2 minutes (if frozen), or until heated through.