01 - Preheat your oven to 350°F. Grease an 8-inch round or square cake pan thoroughly, then line with parchment paper for easy removal.
02 - In a large mixing bowl, whisk together the eggs, neutral oil, brown sugar, Greek yogurt, and vanilla extract. Continue whisking until the mixture is completely smooth and uniform.
03 - Add the flour, baking powder, baking soda, salt, cinnamon, and nutmeg directly into the wet mixture. Using a spatula, gently fold the ingredients together until just combined. Take care not to overmix as this can toughen the crumb.
04 - Fold in the grated carrots until evenly distributed throughout the batter. If using walnuts, pecans, or raisins, add them now and fold gently to incorporate.
05 - Pour the batter into your prepared cake pan. Use an offset spatula or the back of a spoon to smooth the top evenly.
06 - Place the pan in the center of the oven and bake for 35 to 40 minutes. Check for doneness by inserting a toothpick into the center of the cake. It's ready when the toothpick comes out clean or with just a few moist crumbs attached.
07 - Allow the cake to rest in the pan for 10 minutes to set. Then carefully transfer it to a wire cooling rack to cool completely before slicing into servings.