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Preheat the oven to 350°F. Grease an 8" x 2" square pan or a 9" x 2" round pan.
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To make the cake: Stir together the dry ingredients; set aside.
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Whisk together the melted butter or oil, eggs, water, molasses, and vanilla.
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Stir the dry mix into the wet ingredients. Scrape the bottom and sides of the bowl and continue to stir for about 30 seconds, until well blended.
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Fold in the grated carrots, fruit, and nuts.
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Transfer the batter to the pan, smoothing the top with a spatula. Allow the batter to rest for 10 minutes before baking.
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Bake the cake for 35 to 45 minutes, until a cake tester inserted into the center comes out clean.
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Remove the cake from the oven. Allow the cake to rest for 5 minutes before turning out of the pan onto a rack to cool completely before frosting. Alternatively, you can frost and serve the cake right from the pan.
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To make the frosting: Beat the butter and cream cheese until smooth.
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Add the salt and vanilla, then beat in the sugar.
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Beat in an additional teaspoon of milk or cream if the frosting is too stiff to spread; beat in more sugar if it's too thin.
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Spread the frosting over the cake.