For the carrots, sometimes I buy pre-shredded and then give them a good chops so they're a little finer. Otherwise, run the carrots through a fine grate in the food processor. If you like nuts in your cake, add a cup of toasted chopped walnuts or pecans to the batter. Serve the cake with a scoop of vanilla ice cream and drizzle caramel sauce over everything, if you want to get fancy.
Heat the oven to 350 degrees. Brush a 13 x 9 x 2 -inch metal cake pan with olive oil and dust evenly with flour, tapping out any excess flour.
In a medium bowl, whisk the flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt. In another bowl, whisk the olive oil, granulated sugar, brown sugar, yogurt, vanilla, and eggs. Stir in the flour, then add the carrots, pineapple, coconut, and raisins. Pour the batter evenly into the prepared pan.
Bake the cake for 40-45 minutes, or until golden and the cake springs back when touched in the center. Cool completely.
For the frosting, by hand or using a mixer, beat the cream cheese with the butter until smooth. Add the vanilla and 1/3 of the confectioners' sugar and mix until combined. Add the remaining confectioners' sugar (on low speed if using a mixer), and beat until smooth.
Spread the frosting on the cake using an offset knife or back of a large spoon to create deep swooshes. I like to leave the perimeter of the cake with no frosting so the cake can peek through. Chill the cake to set the frosting before serving.