Heat oven to 350°F and butter an 8-inch square baking dish. Whisk eggs, milk and pepper, then stir in diced ham and dried roasted pepper.
Pour into the dish and bake for 20 to 24 minutes until set and 165°F in the center. Rest for 5 minutes, then cut into eight rectangles, each about 2 by 4 inches.
Meanwhile, toast the cut mini-bagel faces in a dry skillet for 1 to 2 minutes per batch, keeping the outside crust soft. Divide Fontina into eight equal portions.
Fold each egg rectangle in half to make a 2-inch square and put on one mini-bagel bottom. Add one cheese portion and close with the top.
Set all eight sliders in a baking dish, cover loosely with foil and bake at 350°F for 5 to 7 minutes until the cheese melts. Serve two per person, removing the foil before bringing the dish to the table.