Set a 10" cast iron skillet over a low flame to warm while everything else is cooking. In a non-stick skillet, cook the sausage patties until done. Meanwhile, beat the eggs until light and frothy.
If necessary, place the first burrito wrap in the warmed cast iron skillet to make it pliable - not too long, because they shrink with heat. You just want to be able to wrap it without cracking or tearing it. Place the wrap on a dinner plate and place two pieces of cheese slightly off center on a diagonal, overlapping slightly. Repeat with the second wrap.
When the sausage patties are done, cut them down the center (to make four pieces). Place half of the sausage patties on each slice of cheese.
Cook the beaten eggs - I make an omelet, or you can scramble them. To this you can add any additional ingredients you want: onions, peppers, bacon, etc. When the eggs are done, divide them in half.
Place one half of the cooked eggs over the cheese and the sausage in the center of each wrap. Pour the enchilada sauce over the eggs. Fold the "short" ends of the wrap inward to encase the fillings. Roll the long way, tucking the ends inward to make tube-shaped wraps. Place seam-sides down in the warm cast iron skillet to toast. Once the seams are toasted and slightly "hardened" I flip them over to melt the cheese inside.