There are many variants on the classic, but as a lover of all things apple, I felt that trying to consume that apple flavor in yet another new way was a worthy effort. The apple cider flavor is subtle, and really only enhances the natural sweetness of the carrot, all while adding to the moistness of the crumb. The maple in the frosting rounds it all out, and makes it, in my opinion, a welcome twist on a timeless treat.
(Note: The frosting is just slightly adapted from Deb Perelman's Maple Cream Cheese Frosting) —Jr0717
Prepare the carrots:
Preheat the oven to 350 degrees and line a baking sheet with parchment. Toss the carrots with 1/4 cup of the cider, and lay out on the parchment. Roast until just slightly tender (you still need to grate these puppies), approximately 15 minutes.
About 7 minutes into the roasting time and when the carrots come out of the oven and are still hot, brush with additional cider (another 1/4 cup of cider is reserved for this). Allow to cool.
Grate the carrots into medium shreds when cool.
Prepare the cake:
(**Only 1/4 cup of the cider goes into the cake batter. If you have remaining leftover from the roasted carrots, feel free to pour into a mug, sprinkle with cinnamon, and sip away!)
Whisk all dry ingredients together in a large bowl, and all wet ingredients** (except the carrots) together in another large bowl.
Add the wet ingredients to the dry, and fold the batter to incorporate. When there are no more clumps of flour or other dry ingredients, add the carrots and mix briefly and gently to distribute.
Line a 12-cavity cupcake tray with liners, and fill each with batter until about three-quarters filled. Bake for approximately 35-40 minutes, or until golden, and a toothpick inserted in the center comes out clean.
While the cupcakes bake, prepare the frosting:
In a stand mixer, beat the butter and cream cheese until roughly combined. Add maple syrup, lemon juice, salt, and half of the sugar, and gently mix to incorporate.
Taste the frosting to see if it is sweet enough - it should have a slight tang to it - and add more sugar if necessary. I prefer to add the sugar slowly to prevent having a cloyingly sweet mess on my hands.
If necessary, frosting can be thinned slightly with additional apple cider.
When the cupcakes have cooled completely, frost each with a piling heap of frosting. When done frosting the cupcakes, any remaining frosting can be eaten from a spatula, spoon, or squeezed out of an icing bag. No one's looking. I promise.