Line a baking sheet with a silicone mat; coat generously with cooking spray. Slice a firm Japanese eggplant 1/16 to 1/8 inch thick using a mandoline. Arrange on the baking sheet in a single layer; coat the eggplant with cooking spray and sprinkle with salt. Bake at 250 degrees F, 50 minutes, rotating the baking sheet halfway through. Flip the slices; continue baking until browned, about 20 more minutes. Transfer the chips to a rack to cool.