Hello Claire. Modifying traditional family recipes can feel a bit daunting, but carrot cake is actually one of the most forgiving bakes when it comes to replacing vegetable oil.
Unsweetened applesauce is widely considered the best substitute. If you want to keep the cake light while preserving that classic homestyle crumb, the ideal approach is a 50/50 split: replace half the oil with unsweetened applesauce and keep the remaining half as oil. For instance, if your recipe calls for 1 cup of oil, you would use 1/2 cup of oil and 1/2 cup of applesauce. You can also replace 100 percent of the oil with applesauce using a direct 1:1 ratio, though doing a full substitution will result in a slightly denser, more sponge-like texture.
In terms of flavor, unsweetened applesauce blends seamlessly with cinnamon, nutmeg, and the natural sweetness of carrots, so you will not notice an overpowering fruit taste at all.
Plain Greek yogurt is another reliable option at a 1:1 ratio. It yields a very tender, moist crumb and adds a gentle tang that pairs wonderfully with carrot cake, especially if you plan to top it with cream cheese frosting.
As for the baking time, pureed fruit and yogurt carry more water than pure fat does. This means the batter may take an extra 3 to 5 minutes to bake thoroughly in the center. I recommend beginning to check your cake with a wooden toothpick about 5 minutes before the recipe's suggested time, and keep it in the oven until the tester comes out clean with just a few moist crumbs attached.
I hope your grandmother's cake turns out wonderfully light and delicious.
