Preheat your oven to 350°F (175°C).

Line a muffin tin with cupcake liners.

In a bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, and nutmeg. Set aside.

In a large bowl, combine granulated and brown sugars.

Add eggs and beat on low speed for about 30 seconds until slightly pale.

Stir in the unsweetened applesauce and vanilla extract.

Slowly drizzle in vegetable oil while mixing until fully incorporated.

Add half of the dry ingredients to the wet mixture.

Toss the shredded carrots with the remaining dry ingredients, then fold them gently into the batter.

Divide the batter evenly among the cupcake liners, filling each about 3/4 full.

Bake for 19-21 minutes, or until a toothpick inserted in the center comes out clean.

Let the cupcakes cool in the tin for a few minutes before transferring them to a wire rack.

Using an electric mixer, beat the butter and cream cheese on medium-high speed until light and fluffy.

Mix in the vanilla extract, then gradually add powdered sugar while beating on low speed until smooth.

Frost the cooled cupcakes using a piping bag or spatula.

Optionally, roll the frosted edges in chopped pecans for added crunch.

Tint marzipan with a few drops of orange gel food coloring and knead until the color is evenly distributed.

Roll small pieces into tapered carrot shapes, dust lightly with cocoa powder to create natural texture, and insert a parsley stem into each.

Gently press these decorative carrots onto the frosted cupcakes.