Instructions

Melt 1 tablespoon butter in 12-inch skillet over medium-high heat. Add apples and cook, stirring often, until just translucent and slightly pliable, 3 to 5 minutes. Transfer to bowl and let cool.
Add cider and dried apples to now-empty skillet and simmer over medium heat until liquid evaporates and mixture appears dry, 15 to 20 minutes. Transfer to separate bowl and let cool.
Adjust oven rack to middle position and heat oven to 325 degrees. Grease 9-inch round cake pan. Whisk flour, baking soda, and salt together in large bowl. In food processor, process dried apple–cider mixture, vanilla, cinnamon, nutmeg, and cloves until smooth, about 30 seconds, scraping down bowl as needed. Add egg and process until combined, about 15 seconds. With processor running, slowly drizzle in 10 tablespoons melted butter. Using rubber spatula, fold pureed apple mixture into flour mixture until combined.
Scrape batter into prepared pan and smooth top. Shingle cooked apple slices around top in decorative circle. Bake until toothpick inserted in center of cake comes out clean, 32 to 35 minutes, rotating pan halfway through baking.
Remove cake from oven and heat broiler. Meanwhile, microwave remaining 1 tablespoon butter and honey until melted, 15 to 30 seconds. Stir in lemon juice and brush mixture over apples. Broil cake, checking often and turning as necessary, until apples are attractively caramelized, 4 to 6 minutes.
Let cake cool in pan for 10 minutes. Run knife around edge of cake to loosen. Invert cake onto plate, then invert again onto wire rack. Let cake cool completely, about 1½ hours, before serving.