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 mixing bowl, whisk together eggs, oil, brown sugar, Greek yogurt, and vanilla extract until completely smooth and well combined.
03 - Add flour, baking powder, baking soda, salt, cinnamon, and nutmeg directly to the wet mixture. Gently fold together until just combined; do not overmix to ensure a tender crumb.
04 - Gently fold in grated carrots until evenly distributed. If using, add nuts and raisins at this stage.
05 - Pour batter into the prepared pan and smooth the top surface. Bake for 35 to 40 minutes, or until a toothpick inserted in the center comes out clean or with a few moist crumbs.
06 - Allow cake to cool in the pan for 10 minutes, then carefully transfer to a wire rack to cool completely before slicing.