Preheat oven to 225°F with 1 oven rack in top third of oven and 1 oven rack in bottom third of oven. Line 2 baking sheets with parchment paper.
Remove core from top 1 inch and bottom 1 inch of each apple. Cut apples crosswise into 1/8-inch-thick slices. Arrange slices in a single layer on prepared baking sheets.
Stir together brown sugar, honey, 1/2 teaspoon water, chile powder, salt, black pepper, and cayenne pepper in a small microwavable bowl. Microwave at high until bubbly, about 20 seconds. Stir and brush over tops of apple slices.
Bake apple slices at 225°F 1 hour; flip apple slices, and rotate pans from top rack to bottom rack. Bake until apple slices are firm and not sticky (they should feel like dried fruit), about 1 more hour. Remove baking sheets from oven. Let cool completely on baking sheets.