Heat a cast iron or non-stick skillet over medium-high heat. Remove the sausage from its casing and form into four equal-sized patties. Cook the patties in the skillet, searing both sides until fully cooked through, about 5 minutes.

While the sausage patties are cooking, reheat the waffles by toasting them on the lightest setting or warming them in the oven. Cut or tear each waffle into fourths to create eight "slices" for the four sandwiches.

Once the sausage patties are cooked, remove them from the skillet and add the butter. After the butter has melted, crack the eggs into the skillet and fry them to your desired doneness (over-medium is recommended). After flipping the eggs, top each one with a slice of cheddar cheese and cook for one minute more.

Assemble the breakfast sandwiches by placing a sausage patty on top of one waffle section. Top the sausage with a cheesy fried egg, then add the other waffle section on top. Use a toothpick or sandwich skewer to secure the sandwich, if needed, and serve immediately.