Heat a skillet over medium heat. While the skillet is warming, assemble your sandwiches.
On two slices of sourdough, layer half of the shredded cheddar cheese, followed by the sliced sausage, and then the eggs.
Crack the eggs into the skillet, cooking them sunny-side up for about 2-3 minutes or until the whites are set but the yolks are still runny. Season with salt and pepper.
Once the eggs are cooked, place them on top of the sausage layer in the sandwiches, then add the remaining cheese on top.
Top each sandwich with the other two slices of sourdough bread to form complete sandwiches.
In the same skillet, melt 1 tablespoon of butter. Once melted, carefully place the sandwiches in the skillet, pressing them down slightly.
Cook for about 3-4 minutes until the bread is golden brown and the cheese begins to melt.
Flip the sandwiches carefully, add the remaining butter to the skillet, and cook for another 3-4 minutes until the other side is golden brown and the cheese is fully melted.
Remove from the skillet, slice in half, and serve immediately while warm.