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 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 wet mixture. Gently fold until just combined, being careful not to overmix.
04 - Gently fold in grated carrots along with walnuts or pecans and raisins if using, until evenly distributed throughout the batter.
05 - Pour batter into prepared pan and smooth the top with a spatula for even baking.
06 - Bake for 35-40 minutes until a toothpick inserted in the center comes out clean or with just a few moist crumbs.
07 - Let cake cool in pan for 10 minutes, then transfer to wire rack to cool completely before slicing.