Preheat your oven to 350°F. Grease and flour a 12"x17" half-sheet pan, or line it with parchment paper.
In a medium bowl, whisk together flour, baking powder, baking soda, salt, and pumpkin pie spice. Set aside.
In a large bowl or in a stand mixer, beat granulated sugar, brown sugar, eggs, vegetable oil, and vanilla extract on medium speed until well combined.
Add the dry ingredients to the wet ingredients. Mix on low speed just until the dry ingredients are incorporated. Don't overmix.
Fold in the carrots, apples, and walnuts (if using).
Pour the batter into the prepared sheet pan and spread evenly with a spatula.
Bake 20-25 minutes or until the top of the cake is golden brown and a toothpick inserted comes out clean. Remove from the oven, and allow the cake to cool completely in the pan.
Using a 2 ½-inch cookie cutter (or your desired shape), cut out circles and arrange the mini cakes on a wire rack. You should have 24 circles when you're finished.
Assemble the mini cakes in this order: 1 mini cake, 2 tablespoons frosting, 1 mini cake on top (lightly press), and another 2 tablespoons of frosting spread on top or piped with an icing bag.
Garnish the cakes as desired. Some options include dusted cinnamon or pumpkin pie spice, candied walnuts, candied pecans, additional shredded carrots, candied carrot strips, fresh berries, edible flowers, edible Easter grass, Easter candy, toasted coconut flakes, lemon zest. You could also color a portion of the frosting with orange and green and pipe a carrot on top.