Preheat the oven to 350°F and line a 12 cup cupcake pan with cupcake liners.
Using the small side of a box grater, finely grate the carrots until you have 1 lightly packed cup. Set aside.
Whisk the cake flour, baking powder, baking soda, cinnamon, nutmeg, ginger, and salt together in a large bowl.
In a separate bowl, whisk the brown butter, granulated sugar, and brown sugar until combined. Then whisk in the eggs, and vanilla extract together until fully incorporated.
Then whisk in the yogurt until combined.
Gently fold in the dry ingredients until just combined.
Then fold in the grated carrots and finely chopped walnuts.
Pour about ¼ cup of batter into each cupcake liner (they should be about halfway full).
Bake at 350°F for 18-22 minutes or until a cake tester comes out clean.
Remove from pan and let cool on wire rack.
Let the carrot cake cupcakes cool completely before frosting.
Cream Cheese Frosting
In a large bowl using a handheld mixer or stand mixer fitted with a paddle attachment, cream the room temperature brown butter and cream cheese together until smooth.
Add in the powdered sugar and mix until fully incorporated.
Mix in the vanilla and beat the frosting on high for 4-5 minutes until light and fluffy!
Add in 1 tablespoon of heavy cream at a time, if needed to thin out the frosting.
Frost the cupcakes with brown butter cream cheese frosting and garnish with chopped walnuts and sugar carrots if desired!
Notes
These cupcakes will keep in the fridge for up to 3 days. However, they taste best at room temperature; so let the refrigerated cupcakes sit on the counter for about 30 minutes before serving.Brown the butter: In a small saucepan, melt unsalted butter over medium heat. Once melted, stir frequently and watch closely for the formation of brown specs on the bottom of the pan and a nutty aroma. Once you see brown specs, stir for just a few more seconds (it browns super quickly). Remove from the heat and immediately pour into a different bowl to prevent it from burning. Let cool to room temperature. I recommend making the brown butter the night before you make the cupcakes, so that it has time to fully cool to room temperature! Note: For every ½ cup (1 stick or 113g), you'll lose about 1 tablespoon (14g) to evaporation while cooking. So you can either add in an extra 1 tablespoon before browning, or if you're browning big batches, just make up the weight difference in your recipe with regular unsalted butter if needed.