Preheat a large nonstick skillet over medium high heat with 2 turns of the pan of olive oil, about 2 tablespoons. Add the breakfast sausage and break it up with the back of a wooden spoon into little chunks, brown sausage for 3 minutes.
Add the sweet potatoes and 3/4 of the chopped red onion to the sausage, season with chili powder, cumin, coriander, salt and pepper, stir frequently and cook for 10 to 12 minutes, or until the potatoes are nice and tender.
While the hash is cooking, in a small bowl combine the tomatoes, jalapeno, and the remaining chopped red onion, cilantro, lime juice and a little salt and pepper.
Once the hash is cooked, add the chopped parsley, stir to combine and transfer hash to a serving platter. Sprinkle with the cheese and cover with aluminum foil, the cheese will melt while you make the fried eggs.
Wipe clean the skillet you made the hash in, return it to the cook top over medium-high heat and add the butter. Once the butter has melted, crack each of the eggs into the skillet, season with a little salt and pepper and fry to desired doneness. Eggs may, of course, be scrambled as well. As you like!
Transfer the fried eggs to the top of the hash, sprinkle with the fresh tomato salsa and serve.