Preheat the oven to 350 degrees F.
Whisk together the flour, baking soda, cinnamon, baking powder, salt, and nutmeg in a medium bowl. In another medium bowl, with an electric mixer on medium speed, beat the eggs, sugar, brown sugar, and canola oil until light and thick. Reduce speed to low and add the flour mixture, beating just until blended. Stir in the vanilla, carrots, and walnuts until well blended.
Line 12 cup cupcake or muffin pan 2/3-full with batter. Bake until the cupcakes are puffed and a toothpick inserted into the center comes out clean, about 20 minutes. Cool the cupcakes completely.
For the frosting: Beat butter and cream cheese at medium speed until creamy (2-3 minutes). Reduce speed to low and add powdered sugar in 2 parts incorporating vanilla extract 1/2 way through and mix until incorporated (scraping down walls with rubber spatula each time). Add cinnamon and fold by hand into frosting. Serve within 24 hours.
Generously frost each cupcake with pastry bag and cut 1/2-inch off the tip. Add edible gold glitter stars if desired.