Preheat the oven to 350°F (180°C). Grease and flour an 8-inch baking pan or a tall 6-inch pan.
Add the eggs, milk, oil, and vanilla to a large bowl and mix until well combined.
In another bowl, combine the flour, cocoa, sugar, baking powder, baking soda, and salt. Add the dry ingredients little by little to the bowl of wet ingredients. Combine just until mixed.
Stir in the boiling water. The batter may be thin, but that's fine.
Fold in the chopped walnuts.
Pour the batter into the prepared pan. Bake for 30 to 35 minutes or until a toothpick inserted into the center comes clean.
Allow the cake to cool in the pan for 10 minutes, then transfer the chocolate walnut cake to a wire rack to cool completely. Once cooled, you can frost the cake with your choice of cream or serve it as is.