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 - Pour in melted coconut oil, Greek yogurt, and vanilla extract. Whisk until the mixture is smooth and homogeneous.
04 - Sift in flour, baking powder, baking soda, salt, cinnamon, and nutmeg. 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 - Pour the batter into the prepared cake pan. Use a spatula to smooth the top surface evenly.
07 - Bake for 35 to 40 minutes, or until a toothpick inserted into the center of the cake comes out clean with no wet batter attached.
08 - Allow the cake to cool in the pan for 10 minutes, then carefully transfer to a wire rack to cool completely.
09 - Once cooled, optionally dust with powdered sugar or top with Greek yogurt frosting before slicing and serving.