01 - Preheat the 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 the batter into the prepared pan and smooth the top with a spatula.
06 - Bake for 35–40 minutes, or until a toothpick inserted in the center comes out clean or with a few moist crumbs.
07 - Allow the cake to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely before slicing.