Start by getting everything ready. Preheat the oven to 350°F (175°C). Grease your baking pan well, and if you want easier removal later, line it with parchment paper. Grate the carrots with a box grater and set them aside.
In a large mixing bowl, beat the softened butter together with the granulated sugar and brown sugar until it turns light, fluffy, and creamy—this usually takes two to three minutes with an electric mixer.
Next, crack in the egg and pour in the vanilla extract. Mix until everything is smooth and well blended.
In another bowl, whisk together the flour, baking soda, salt, cinnamon, ginger, and nutmeg. Stir in the rolled oats so they’re evenly coated with the dry mixture.
Now, slowly add the dry ingredients into the butter mixture, mixing on low speed just until the flour disappears. Don’t overmix this keeps the cake tender. With a spatula, gently fold in the grated carrots until they’re evenly spread throughout the batter.
Pour the batter into your prepared baking pan and smooth it out. Bake for about 28 to 32 minutes, or until a toothpick poked in the center comes out clean. Let the cake cool on a wire rack before adding any frosting.
While the cake cools, make the frosting. Beat softened butter and cream cheese together until light and fluffy. Add the powdered sugar gradually, one cup at a time, mixing well after each addition. Finish it off with vanilla extract, and beat until smooth and creamy.
Once the cake is fully cooled, spread the cream cheese frosting evenly over the top using a spatula. Slice, serve, and enjoy.