Heat skillet (preferably a cast-iron) over medium heat. Add sausage and cook until brown, about 5 minutes.
Add in onion, jalapeño, salt, and pepper to the browned sausage. Cook another 3-5 minutes, until onion is soft. Remove from heat and transfer sausage mixture to a paper towel lined plate.
Add salt, pepper, and optionally add cayenne pepper to your sweet potatoes
Heat skillet to medium-high heat and add butter to the pan. Once the butter melts, add the cubed sweet potato. Stir frequently and pay close attention so you don't burn the sweet potato. If the edges seem to be turning black fast, turn the heat down to medium. This should take about 10-15 min, or until potatoes are no longer crunchy in texture when eating.
When potatoes are no longer hard in texture, turn the temperature down to low, and thoroughly mix in sausage, jalapeño, and onion mixture. Once all is mixed, do not stir anymore. This is the part to make a nice crispy hash bottom. After about 5 minutes top with your shredded cheddar, and make sure some of the cheese is directly touching the skillet to get that crispy cheese. Allow to cook for another 5 minutes, or until the bottom is nice and crispy.
Note: If it seems like the hash is getting too crisp, or starting to turn black, then just remove the pan from heat, but allow to sit for 5-10 minutes. As the pan slowly cools (especially if you're using a cast iron) it will still crisp the hash, but slower.
While the hash is crisping, heat olive oil in another skillet over medium heat to fry your eggs. Crack your eggs into the skillet once it's hot and cook your eggs to desired doneness: sunny-side up, over easy, over medium, over hard.
After hash is crisp, use a stiff spatula (I like a nice metal one for cookies) to dislodge hash from the pan and set the hash onto a paper towel to remove excess grease. Divide hash evenly and serve onto plates, and then top with fried eggs, sour cream, and hot sauce of your choice. Enjoy!