Preheat oven to 350 F degrees. Spray a 9 inch round baking pan with non-stick spray and set aside. I used a spring form pan and it was big enough, if using regular cake pans you can divide the batter into 2 pans.
Grate the carrots finely using a food processor or using a hand grater. Set aside.
In a bowl sift together all purpose flour, baking powder, baking soda, salt and cinnamon powder. Set aside.
In steel bowl of your stand mixer fitted with paddle attachment or using your hand mixer beat together oil and sugar till well combined.
Add in the yogurt and mix.
Now start adding the flour mixture alternating with buttermilk. Add flour in 3 parts and buttermilk in 2 parts starting and ending with flour. Mix till batter is smooth but do not overmix.
Finally fold in the shredded carrots.
Pour batter in prepared pan and bake at 350 F degrees for 35-40 minutes or till a toothpick inserted in the center comes out clean.
Cool the cake completely before frosting it.
In the steel bowl of your stand mixer fitted with paddle attachment or using your hand mixer beat butter and cream cheese together till smooth and creamy.
Add vanilla and mix.
Start adding confectioners sugar 1/2 cup at a time, beating well after each addition.