Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish; set aside.

Mix together sugar, oil, buttermilk, eggs, and 1 teaspoon vanilla in a large bowl until well combined. Stir in carrots, pineapple, and coconut. Combine flour, baking soda, cinnamon, and salt in a medium bowl; gently stir into carrot mixture. Mix in nuts until incorporated. Spread batter into the prepared dish.

Bake in the preheated oven until a toothpick inserted into cake comes out clean, about 55 minutes. Remove from the oven and set aside to cool.

Beat together confectioners' sugar, cream cheese, butter, and remaining 1 teaspoon vanilla in a large bowl with an electric mixer until creamy. Frost cooled cake while still in the dish.