Preheat your oven to 350°F (175°C) and line your muffin tin with cupcake liners.

In a large bowl, whisk together the all-purpose flour, baking powder, baking soda, ground cinnamon, nutmeg, and salt.

In a separate bowl, cream together the softened unsalted butter, granulated sugar, and brown sugar until light and fluffy. Add eggs one at a time, mixing after each. Fold in grated carrots and vanilla.

Gradually add the dry ingredients to the wet mixture, folding gently until just combined. Avoid overmixing.

Fill each cupcake liner two-thirds full with the batter.

Bake for 18 to 22 minutes, until a toothpick comes out clean. Let cool in the pan for 5 minutes before transferring to a cooling rack.

For the frosting, beat cream cheese and softened butter until smooth. Gradually add powdered sugar and vanilla until fluffy.

Frost the cooled cupcakes with the cream cheese frosting and add any optional toppings.