01 - Preheat oven to 350°F. Grease and line an 8-inch round or square cake pan with parchment paper.
02 - In a large bowl, whisk together eggs, oil, brown sugar, Greek yogurt, and vanilla extract until smooth and well combined.
03 - Add flour, baking powder, baking soda, salt, cinnamon, and nutmeg directly to the bowl. Gently fold together until just combined; do not overmix.
04 - Fold in grated carrots, and if using, nuts and raisins, until evenly distributed throughout the batter.
05 - Pour batter into prepared pan and smooth the top. Bake for 35-40 minutes until a toothpick inserted in the center comes out clean or with a few moist crumbs.
06 - Let cake cool in pan for 10 minutes, then transfer to wire rack to cool completely before slicing.