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 pale.
03 - Pour in melted coconut oil, Greek yogurt, and vanilla extract. Whisk until the mixture is smooth and emulsified.
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, distributing evenly throughout the batter.
06 - Pour batter into the prepared pan. Smooth the top with a spatula to ensure even baking.
07 - Bake for 35 to 40 minutes, or until a toothpick inserted in the center comes out clean.
08 - Let cool in the pan for 10 minutes, then transfer to a wire rack to cool completely before serving.
09 - Dust with powdered sugar or top with Greek yogurt frosting before serving, if desired.