Preheat your oven to 350°F (175°C). If using turkey or chicken sausage, slice it into small, bite-sized pieces.

In a skillet over medium heat, melt a tablespoon of butter. Add the sausage pieces and cook until golden brown and cooked through, about 5-7 minutes. Remove and set aside.

In a large bowl, crack the eggs and beat until well mixed. Season with salt and pepper. In the same skillet, add another tablespoon of butter and pour in the beat eggs. Cook while gently scrambling, until the eggs are set but still slightly soft, about 3-4 minutes.

Once the eggs are cooked, fold in the cooked sausage and half of the shredded cheese. Stir until evenly combined.

Slice the Hawaiian rolls in half. In a baking dish, lay the bottom halves of the rolls and spoon the egg and sausage mixture evenly on top. Sprinkle the remaining cheese over each sandwich and place the top halves of the rolls back on.

Cover the baking dish with foil and bake for 15 minutes. Remove the foil and bake for an additional 5-10 minutes until the cheese is melted and bubbling.

Remove from the oven, allow to cool for a minute, slice into individual sandwiches, and serve warm.