Preheat oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a large bowl, cream together the applesauce/oil and sugar until light and fluffy.
Beat in the eggs one at a time, then stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking soda, baking powder, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Be careful not to overmix.
Fold in the carrots, coconut, nuts (if using), and pineapple.
Pour batter into the prepared pan and bake for 30-35 minutes, or until a wooden skewer inserted into the center comes out clean.
Let the cake cool completely before frosting. For the frosting, beat together the softened butter and cream cheese until smooth. Gradually add the powdered sugar and vanilla, beating until light and fluffy. Frost the cooled cake and top with toasted pecans or coconut, if desired.