Cook the sausage patties in a non-stick skillet over medium heat. Cook until browned and no pink remains. remove from skillet and drain on a paper towel
In the same skillet, fry the eggs in melted butter. Cook the eggs unit the whites are set but yolks are stilly runny (or to your desired doneness)
Butter four slices of brioche on one side. Add cooked sausage to two slices of bread and cheese to the other slices of bread. Toast the four slices butter-side down for 3-4 minutes. Add one egg to each of the sausages, then place the cheese side on top of the egg/sausage side. add more butter to the pan and grill the sandwich until the cheese is melted. Serve immediately