Special equipment: 18 cupcake liners; a piping bag
For the cupcakes: Preheat the oven to 350 degrees F. Line two standard muffin tins with 18 cupcake liners.
Into a large mixing bowl, sift together the flour, sugar, brown sugar, baking powder, baking soda, cinnamon, nutmeg, ginger and salt.
In the bowl of a stand mixer or in a medium bowl using a hand mixer, whip the eggs until they thicken and ribbons form when the beater is lifted, 3 to 5 minutes. Slowly add the oil, vanilla and marmalade to the whipped eggs. Gently fold the liquid mixture into the dry ingredients to form the batter; it may feel a little thick. Add the shredded carrots and gently but evenly fold them into the batter.
Distribute the batter among the cupcake liners. Bake until a toothpick comes out clean, 12 to 15 minutes.
For the frosting: In the bowl of a stand mixer or in a large bowl using a hand mixer, beat the cream cheese and butter until well blended and lightened in texture. Beat in the sugar and vanilla until blended. Beat in the food coloring of your preference if using.
Transfer the frosting to a piping bag. Pipe onto the cupcakes in a swirl.