My solution to the vegetable oil dilemma is to use melted BUTTER! In my experience, butter provides the required moisture and richness of oil without becoming too dense. The cake comes out just a bit lighter with a more delicate crumb. If you prefer a slightly lighter texture to your carrot cake than this recipe is for you.
Wait! I haven't told you about the extra little step that will make your cake really stand out. You need to do a little more to your butter than simply melt it on the stovetop. You need to BROWN YOUR BUTTER! When you allow butter to gently heat up past its melting point, it will slowly begin to brown. As the milk-solids in the butter turn brown, they cause the butter to take on a wonderful nutty flavor and aroma. The French refer to this type of butter as "beurre noisette". I'm sure it has something to do with the hazelnut flavor the butter contains when you're done. I think the browned butter makes this cake so good that it doesn't even need the cream cheese icing. But as you can see in the pic above, I can't resist a good cream cheese icing. Besides, a birthday cake just doesn't seem complete without the icing.
Well, that's the secret. Click "Read More" below for the recipe. Now go brown some butter and bake a cake! Enjoy!