Put sweet potatoes and water in a skillet and bring to a boil over high heat.

Reduce heat to low and cook about 20 minutes, stirring occasionally, until the water has been absorbed by the sweet potatoes.

Add oil, sausage, onion, bell pepper, and garlic to the skillet with the sweet potatoes. Cook about 20 minutes, stirring occasionally, until the onion is lightly browned and the sweet potatoes are tender.

Divide the hash between 4 plates and return the skillet to the stove.

Reheat the skillet over medium-high heat and when it is hot, add the remaining 1 teaspoon oil.

Add the eggs, one at a time, and cook about 3 to 5 minutes until the whites are solid and the yolks begin to thicken but are not hard. Flip the egg and cook for one more minute.