Mix the cake flour, sugar, baking powder and salt together in a bowl.
In a mixing bowl, combine the milk, butter and vanilla.
With the mixer on low speed, slowly add the dry ingredients until they are just incorporated.
Increase the mixer speed to medium and add the egg. Beat the cake mix for 2 minutes, then add the walnuts and beat for one more minute.
Make the chocolate sauce
In a small saucepan, combine the cocoa powder, sugar, water and vanilla. Heat the mixture over low heat until the cocoa and sugar is dissolved.
Build and bake the pie
Pour the batter into the prepared pie shell, then carefully drizzle the chocolate sauce over the cake batter.
Bake the pie for 45-55 minutes in a 350 degree oven. The pie is done when a toothpick inserted into the middle comes out clean. If the crust starts to brown, you can cover it with a bit of foil.