Form sausage into six equal sized patties. Cook according to package instructions, until browned and cooked through (about 15 minutes). Transfer cooked sausage to a paper towel-lined plate to drain.
While sausage is cooking, melt ½ tablespoon butter in a 12-inch skillet over high heat.
Whisk together three eggs in a small bowl. Pour into hot skillet; reduce heat to medium and cover with lid.
Cook eggs until slightly set, then lift the edges so the raw egg on top runs underneath. Continue cooking until eggs are completely set. Fold the cooked eggs into thirds (first folding one side, then the other, into the center). Cut into three equal portions. Transfer to a plate.
Repeat previous step. (You should end up with six equal-sized egg portions.)
Assemble sandwiches: onto six slices of Swirl Bread, stack one slice of American cheese, one sausage patty, one egg portion, and a second slice of Swirl Bread.
Try this recipe variation: swap the breakfast sausage for bacon or thick-cut ham or Canadian bacon.