Form the sausage into four thin square patties slightly larger than the bread slices.
Cook the patties in a skillet over medium heat for 4 minutes per side until browned and 160°F, then transfer them to a rack.
Melt half the butter in the sausage drippings and griddle the bread in two batches until golden on one side.
Add the remaining butter, fry the eggs over-medium and season with salt and black pepper until they reach 160°F.
Layer four toast slices with sausage, egg and cheddar, then close with the remaining toast.
Return the sandwiches to the skillet for 1 minute per side until the cheese softens.