Preheat the oven to 425° F. Line a large baking dish with parchment paper.
Place the peeled sweet potatoes on a work surface. Using two wooden spoon handles as a guide along both long sides of one potato (to prevent the knife from slicing all the way through the potato), slice the potato crosswise into very thin slices that go at least three quarters of the way through.
Gently slide one very thin garlic slice between every other slice in the sweet potato (the garlic slices will help to hold the sweet potato slices slightly apart). Repeat with the remaining potatoes and garlic slices.
In a small bowl, whisk the oil, chili powder, and salt to blend. Using a pastry brush, generously brush the mixture all over the potatoes.
Place the potatoes in the prepared dish. Brush the mixture again over the tops of the potatoes a couple of times, allowing the oil to drip between the slices (some of the oil mixture might be left over).
Bake until the sweet potatoes are tender all the way through and the tops of the slices are beginning to get crusty and golden brown, 1 hour 10 minutes to 1 hour 15 minutes. Serve warm or at room temperature.