To prepare the filling, in a bowl, beat together the egg and milk until smooth. Stir in the ham, onion, cheese, salt and pepper. Set aside.

To prepare the biscuits, preheat the oven to 450°F. Generously coat a muffin pan with nonstick cooking spray.

In a large bowl or a food processor, combine the flour, baking powder, baking soda and salt. Stir or pulse until blended. Cut the butter into chunks and cut them into the flour mixture until it resembles coarse meal. (One trick is to cut up the butter beforehand and keep it in the freezer until needed.) Add the milk to the flour mixture and mix until just combined.

Transfer the dough to a floured surface. Fold it 5 or 6 times, keeping it floured just enough so it does not stick. Using your fingers, press the dough into a 12-by-9-inch rectangle about 1/4 inch thick. Cut the dough into 3-inch squares and drape each in the prepared muffin pan. Don’t press them down completely, nor worry about covering the entire muffin cup. 

Spoon the filling into the middle of each dough square, starting lightly and adding more if necessary. Pull the 4 points of each square to the middle but do not completely enclose the filling, as the biscuits will rise and fill out during baking. Bake for 12 to 14 minutes. Serve hot and garnish with shredded cheese.