Preheat oven to 350F. Grease and dust two 8 inch round cake pans or 9x13 inch pan.
In a deep bowl, beat eggs and vanilla then add both brown and white sugar and continue beating.
Add oil then apple sauce and mix well.
In another bowl, combine flour, baking powder, baking soda, salt and cinnamon.
Gradually add the flour mixture to the wet ingredients and mix.
Finally fold in the carrots and pecan if using.
Bake in the prepared pan(s) until done.*
Meanwhile, prepare the frosting. In a bowl beat cream cheese, yogurt and honey until well combined. Refrigerate until the cake is done and cooled.
If you are making a two tier cake, add half the filling over one cake and cover with the other one.
Decorate with the rest of the frosting.
Refrigerate to set for a couple of hours before serving.