Preheat the broiler to high heat.
Melt the butter in a heavy-bottomed pan over medium-high heat. Cook the bacon in the butter until it has caramelized, and then set aside.
Remove some of the grease from the pan, and then cook the egg to over easy, keeping the yolk intact. Cook the ham alongside the egg until browned.
Slice the donut in half bagel-style. Lay a slice of Cheddar on the inside of each half and place under the broiler until the cheese is gently softened and just beginning to melt. Top one donut half with the ham, followed by the bacon, egg and potato sticks and finish with the second donut half.
This recipe was provided by a chef, restaurant or culinary professional and may have been scaled down from a bulk recipe. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.