Melt 4 tablespoons butter in a large skillet over medium-high heat. Add 4 sage leaves and fry quickly until crisp, about 30 seconds. Transfer to a paper towel lined plate to drain. Reserve.
Add the sweet potatoes to the skillet, toss until coated in the butter, then add the water and the remaining 8 sage leaves. Bring the water to a simmer and cook the potatoes, uncovered, until the water has evaporated and the potatoes are just fork tender, about 10 minutes. If there is any excess water in the pan, remove it with a large spoon and reserve. Continue cooking the potatoes, scraping the pan frequently with a spoon, until crusty brown, about 10 more minutes. Add a tablespoon of the leftover cooking liquid or fresh water if the potatoes stick or begin to scorch.
Meanwhile, melt 2 tablespoons of the butter in a medium skillet over medium heat. Add the chopped onion and cook, adding water as necessary when the pan gets dry, until deep golden brown, about 20 minutes. Transfer the onions to a serving bowl. Wipe out the pan, add the remaining 2 tablespoons butter, and fry the eggs, 2 at a time, to your preference. Cook's Note: I like mine over easy.
Plate the potatoes in the center of 4 plates with the caramelized onions alongside. Top each plate with 2 fried eggs, garnish with a fried sage leaf and enjoy!
Cook's Note: Serve with your favorite breakfast meat.