yes this is what we are going to do first. why you ask? because brown butter takes some time to cool completely. 

• melt the butter gently in a pan on medium heat
• when butter starts to foam, whisk continuously
• when brown bits start to form - remove from heat
• let it cool for about 40-45 minutes before using it

• combine all dry ingredients (flour + baking powder+ natron + chai spices) and set aside
• take sugar in oil and mix until combined
• add one egg at the time and mix until combined
• add one cup of dry ingredients and one tablespoon of yoghurt - do not overmix. it only needs to be combined. 
• continue until no dry ingredients and no yoghurt are left. 
• take your shredded carrots and fold them into the dough.
• bake the cake for 40-45 minutes at 175°C
• let the cake cool completely !

• combine butter and cream cheese and mix until creamy ( It may seem it is never going to get creamy, but just mix for about 4-5 minutes - it will get there)
• pour in sifted powdered sugar, one cup at the time
• the cream cheese will start to get creamier and thicker (if its to thick add 2 tablespoons of milk) 

• take your cake and put the cream cheese on top
• use some walnuts for decoration