In a large skillet, heat the oil over medium heat. Add the diced onion and cook for 4–5 minutes until softened.
Add the breakfast sausage and cook until browned, breaking it into crumbles. Drain any excess grease.
In a separate bowl, crack eggs and add milk, salt and pepper. Whisk to combine then pour over sausage in a hot pan. Scramble the eggs until set and well combined with the sausage.
Slice the Hawaiian rolls in half horizontally, keeping them connected. Place the bottom half in a greased 9x13-inch baking dish.
Mix the softened butter and maple syrup together, then spread some on the bottom half of the rolls
Spread the scrambled eggs evenly over the rolls, followed by the sausage mixture. Lay the cheddar cheese slices on top.
Place the top half of the rolls over the cheese.
Slather more maple butter all over the top then cover with foil.
Bake for 12–15 minutes, or until the cheese is melted.
Remove foil and bake for 5 more minutes until tops are golden.