Start by heating the oven to 350°F (175°C). Prepare your pan by greasing it and lightly dusting with flour or you can line it with parchment paper for easier removal later.
Take a bowl and put in the flour, baking soda, cinnamon, and salt. Mix these ingredients together and set them aside.
In another bowl, whisk the eggs with the sugar and oil until the mixture looks smooth. Add the vanilla, crushed pineapple, and Amish sourdough starter, stirring until everything is combined.
Slowly add the dry ingredients to the wet mixture, stirring gently so that the batter comes together without becoming too dense.
Carefully fold in the grated carrots, nuts, and shredded coconut, making sure they are evenly distributed.
Pour the batter into the prepared pan and spread it out evenly. Place it in the oven and bake for about 40–50 minutes. Check by inserting a toothpick in the center; it should come out clean when the cake is ready. Let the cake cool in the pan on a wire rack until it reaches room temperature.
For the frosting, beat the softened cream cheese and butter until smooth. Slowly add powdered sugar and vanilla, continuing to beat until the frosting is light and fluffy.
Once the cake has cooled completely, spread the frosting over the top. You can sprinkle extra nuts or coconut on the frosting if you like. Cut the cake into pieces and enjoy.