Place the patties on a foil-lined baking sheet and cook to an internal temperature of 160°F using a thermometer, flipping over once about halfway through cooking.
Add the oil in a non-stick pan over medium heat. Crack the eggs into the pan and cook until the whites are nearly set. Break the yolks and gently flip over with a spatula. Cook for another 30 seconds.
Lightly toast the bread.
Place the sausage, cheese, and eggs on the bread. Place the sandwich on a baking sheet and bake in the oven for about 3 to 5 minutes, or until the cheese is melted. Cut in half and serve with strawberries.