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 lightened in color.
03 - Pour in melted coconut oil, Greek yogurt, and vanilla extract. Whisk until the mixture is smooth and emulsified.
04 - Sift flour, baking powder, baking soda, salt, cinnamon, and nutmeg directly into the wet mixture. Fold gently with a spatula until just combined, taking care not to overmix.
05 - Gently fold in grated carrots along with nuts and raisins if using until evenly distributed throughout the batter.
06 - Pour the batter into the prepared cake pan. Use an offset spatula or the back of a spoon to smooth the top evenly.
07 - Bake for 35 to 40 minutes, or until a wooden toothpick inserted into the center emerges 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 serving.
09 - If desired, dust the cooled cake with powdered sugar or frost with Greek yogurt frosting before slicing and serving.