Preheat your oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a large bowl, beat together the eggs, sugar, and vegetable oil until well combined.
Stir in the grated carrots and vanilla extract.
In a separate bowl, combine the all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg.
Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Fold in the chopped walnuts.
Pour the batter into the prepared baking pan and spread it evenly.
Bake in the preheated oven for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean. Allow the cake to cool completely in the pan.
To make the chocolate frosting, melt the butter in a medium saucepan over low heat.
Stir in the cocoa powder until smooth.
Gradually add the powdered sugar and milk, beating with a hand mixer until smooth and spreadable.
Stir in the vanilla extract.
Spread the chocolate frosting evenly over the cooled cake.
Sprinkle with chocolate chips.