In a small pot, start browning your butter. Slowly stirring it, watch how it will start changing colour to golden brown. Take it off the heat once you start smelling a nutty aroma and leave it on the side to cool.
Preheat your oven at 180℃ and line your baking pan with parchment paper.
In a medium bowl, add the flour, baking soda, nutmeg, cinnamon and salt. Set it aside.
In a large bowl, add the browned butter, sugar, eggs, buttermilk and applesauce (or yoghurt). Whisk until everything is well combined.
Gradually add the dry ingredients into the wet ones and stir until everything is incorporated. Lastly, fold in the shredded carrots and walnuts.
Bake this for 25-30 minutes or until a toothpick comes out clean from the middle of the cake.
While the cake is baking, start on your frosting. Grab a large bowl and mix cream cheese with the butter on medium-low heat until it's smooth and creamy - about 2-3 minutes.
Add salt, vanilla extract, cinnamon powder and mix. Lastly, add the powdered sugar and fold until everything's incorporated.
Once the cake is out, allow it to rest in room temperature for 20-30 minutes and then add the frosting on top. Slice and enjoy!