A variation on “shirred” (baked) eggs. The flavorings are limited only to your imagination.
Step 1: Set up your grill for direct grilling and preheat to medium-high (400 degrees).
Step 2: Grease a small ovenproof skillet, baking dish, or ramekin (see Note below) with 1/2 tablespoon of the butter or olive oil. Crack in the eggs and sprinkle the ham or bacon (if using) on top. Pour the cream over them. Sprinkle with the cheese and breadcrumbs. Dot the tops of the eggs with the remaining butter or oil.
Step 3: Place the skillet with the eggs on the grill away from the heat. Toss the wood chips on the coals or place in the smoker box of your gas grill. Indirect grill until the crumbs are browned and the eggs are just set, 7 to 10 minutes. (The yolks should remain a little runny in the center.) Serve the eggs at once with strips or slices of fire-grilled toast.
There are several options for cookware. I like mini-cast iron skillets, but you can also use ramekins or small cazuelas (shallow Mexican earthenware dishes).