Place some breakfast sausage into the palm of your hand, pressing into a flat shape. Next, place a potato in the center of the sausage and wrap it around to cover the potato completely, forming it into an egg shape.
Roll the "egg" in flour, beaten egg, and breadcrumbs, then set aside on a tray. Repeat with the rest of the potatoes.
Place oil in a deep-fryer, or heavy pot (I used a wok) and heat over medium-high heat. When the oil is hot, add the Scotch Potato "Eggs" carefully, with a metal skimmer, or similar tool, a few at a time, turning often until they are golden brown in color, and the sausage is completely cooked.
Remove from oil and place on paper-towel lined plate. Continue to fry the remaining Scotch Potato "Eggs." Let cool slightly and serve hot or cold as desired: breakfast, brunch or lunch; also makes a great item for travelling, or for a picnic, snack or a side-dish.