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 and melted butter 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, combine the cider, maple syrup, cinnamon, apples and remaining tablespoon butter in a medium pot over medium-high heat. Bring to a boil, then cover and cook until the apples are soft, about 20 minutes. Uncover, mash with a potato masher or the back of a fork and continue to cook until most of the liquid has evaporated and it has the consistency of chunky applesauce, about 5 minutes. Stir in the figs and let cool slightly. Divide the applesauce among the toasts and sprinkle with the granola. 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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