Preheat Oven: Set your oven to 350°F (175°C). Grease a 13x9 inch baking pan or line it with parchment paper.
Mix Wet Ingredients: In a large bowl, beat together the vegetable oil and white sugar. Incorporate the sourdough starter gently. .
Add Eggs. Add the eggs one at a time, thoroughly mixing after each addition. Stir in the vanilla extract.
Add Fruits and Carrots. Reduce mixer speed and mix in the grated carrots, drained crushed pineapple, and golden raisins.
Dry ingredients. Add the all-purpose flour, cinnamon, allspice, salt, and baking soda. Gradually add the dry ingredients to the wet mixture, stirring gently until just combined.
Bake. Pour the batter into the prepared pan, spreading evenly. Bake for 40-50 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool completely in the pan on a wire rack.
Make the Frosting. Beat together the cream cheese, melted butter, and vanilla extract. Gradually add powdered sugar and salt (if using unsalted butter), beating until smooth. If necessary, thin with milk or cream to reach desired consistency.
Frost the Cake. Once the cake is completely cooled, spread the frosting evenly over the top.