Add the bacon to a 10-inch non-stick skillet and cook over medium-high heat, stirring regularly, until the bacon is crispy, about 10 minutes. Using a slotted spoon, remove the bacon to a paper towel-lined plate.
In a large bowl, add the eggs, 1/4 cup of water and 1/2 teaspoon each salt and pepper. Set aside.
Drain off all but 2 tablespoons of the bacon fat from the skillet. (If the bacon has not rendered enough fat, add 2 tablespoons of olive oil instead.) Return the skillet to medium-high and add the sweet potato, 1/4 teaspoon each salt and pepper and cook, stirring, until the potato is slightly browned and fork tender, 7 to 10 minutes. Add in the kale and a small pinch each of salt and pepper and cook, stirring, until wilted, about 4 minutes. Add the bacon back to the skillet. Turn the heat down to medium-low and add the egg mixture and half of the Cheddar. Using a rubber spatula, start lightly scrambling the eggs. When the edges begin to set, top with the remaining Cheddar and transfer the skillet to the oven. Bake until the egg is set and lightly puffed up, 5 to 7 minutes
Remove from the oven and let cool for 5 minutes. Slice into wedges and serve.