Preheat the oven to 450 degrees F.
Slice off the 4 long sides of each of the sweet potatoes so the potatoes are squared off and sit flat on a cutting board. Slice the potatoes lengthwise into 1/2-inch-thick planks, about 5-inches-by-2-inches (you should get 3 planks per sweet potato). Combine the sweet potatoes, olive oil and a pinch of salt in a medium bowl and toss gently to coat. Spread them out on a baking sheet and roast, flipping halfway through, until lightly browned and tender when pierced with a knife, about 15 minutes. Remove the sweet potato toasts to 2 plates.
Meanwhile, heat a medium nonstick skillet over medium heat. Cook the bacon, stirring occasionally, until crisp and browned, 8 minutes. Remove to a paper towel. Reserve the pan, and discard all but 1 tablespoon of the bacon fat.
Sprinkle the eggs with 1/4 teaspoon salt. Add the eggs to the pan, then immediately lower the heat and cook, stirring once and swirling the pan to cover with the egg. Let cook untouched, 1 minute, then lightly lift the eggs and swirl uncooked egg around the pan and let cook, 1 minute more. Sprinkle the cheese over the eggs, then cover and cook until the eggs are just set and cheese is melted, 30 seconds to 1 minute. Sprinkle the bacon on top of the cheese. Transfer the eggs to a cutting board and cut into 6 pieces. Divide the eggs among the toasts and top with a couple grinds of pepper. Serve immediately.
You can make the toasts in advance and refrigerate them in an airtight container up to 4 days. Reheat in a toaster until warmed through.
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