Step 1
Preheat the oven to 400°F/200°C. Grease 16 cups in two shallow muffin pans.
Step 2
Roughly grate 1 apple. Cut the remaining apple into 1/4-inch/5-mm-thick slices and toss in the lemon juice. Sift the flour, baking powder, and cinnamon into a large bowl, then stir in the brown sugar and grated apple.
Step 3
Combine the melted butter with the milk, apple juice, and egg. Stir the liquid ingredients into the dry ingredients, mixing lightly until just combined.
Step 4
Spoon the batter into the prepared pans and arrange 2 of the apple slices on top of each cupcake. Bake in the preheated oven for 15–20 minutes, or until risen, golden, and firm to the touch. Transfer to a wire rack and let cool.
Step 5
For the caramel sauce, place all the ingredients in a small saucepan and heat, stirring, until the sugar is dissolved. Increase the heat and boil rapidly for 2 minutes, or until slightly thickened and syrupy. Cool slightly, then drizzle over the cupcakes and let set.
Step 6
Adapted from <a href="http://www.amazon.com/gp/product/1445438070/ref=as_li_qf_sp_asin_il_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=1445438070&linkCode=as2&tag=craftfocom-20">"The Cupcake: Life's Better With a Cupcake,"</a> published by Parragon Books.