With a fork, prick the sweet potatoes well all over. Place them on a paper towel in a microwave oven. Cook them for 5 minutes (10 if they're really big). Remove them and let them cool for 10 minutes (the potatoes will be partially cooked).
When the potatoes are cool enough to handle, cut them into 1/4-inch chunks; set aside.
Cook the bacon until it is browned and chewy, but not crisp, or brown the sausages. Transfer to a plate lined with paper towels.
In the same skillet, add the oil and when it is hot, cook the onion and sweet potato chunks for 5-10 minutes or until they are tender and golden.
Add the sage, thyme, salt, and pepper. Cook another 1 to 2 minutes, and add more salt and pepper.
Meanwhile, in a large nonstick skillet, heat the butter. When it is hot, add the eggs, salt, and pepper. Fry them until the whites are firm.
Divide the hash among 4 large plates. Add an egg and some bacon/sausage to each one.