Preheat your oven to 350°F (175°C). Line a 12-cup muffin tin with parchment cupcake liners and set it aside.
In a large bowl, whisk together the room temperature eggs, brown sugar, and granulated sugar until the mixture is smooth. Stir in the unsweetened applesauce and vanilla extract.
In a separate bowl, gently whisk together the all-purpose flour, baking powder, ground cinnamon, and salt.
Gradually add the dry flour mixture to the wet ingredients, stirring until just combined. Be careful not to overmix!
Fold in the shredded apples until they are evenly distributed throughout the batter.
Divide the batter evenly among the 12 prepared muffin cups. Bake for 25 to 30 minutes, or until a toothpick inserted into the center of a cupcake comes out clean.
Transfer the baked cupcakes to a wire rack and let them cool completely before you add the frosting.
Unwrap the caramels (or use convenient caramel bits) and place them in a microwave-safe bowl with the heavy whipping cream.
Heat in the microwave at 50% power for 1 minute. Stir well. Continue heating in 30-second bursts at 50% power, stirring after each, until the caramel is smooth and fully melted.
Once the cupcakes are completely cool, spoon a generous layer of the warm caramel frosting over the top of each one. If the caramel starts to get too thick, pop it back in the microwave for another 30 seconds at 50% power and stir before continuing.
For a fun touch, add a mini popsicle stick to each cupcake!