01 - Preheat the oven to 350°F. Grease and line an 8-inch square or round cake pan with parchment paper.
02 - In a large mixing bowl, whisk together eggs and sugar until well combined and slightly thickened.
03 - Add melted coconut oil, Greek yogurt, and vanilla extract to the egg mixture. Whisk until smooth and fully incorporated.
04 - Sift flour, baking powder, baking soda, salt, cinnamon, and nutmeg directly into the wet ingredients. Fold with a spatula until just combined, being careful not to overmix.
05 - Gently fold in grated carrots, nuts, and raisins if using, until evenly distributed throughout the batter.
06 - Transfer batter to the prepared pan, spreading evenly and smoothing the top surface with a spatula.
07 - Bake for 35-40 minutes, or until a wooden toothpick inserted into the center comes out clean or with just a few moist crumbs.
08 - Allow the cake to cool in the pan for 10 minutes, then carefully transfer to a wire rack to cool completely before frosting or serving.
09 - Dust with powdered sugar or top with Greek yogurt frosting before serving, if desired.