Preheat oven to 375 degrees F (190 degrees C). Grease and flour an 8-inch square baking pan.
In a medium bowl, sift together the flour, cocoa, baking powder, baking soda, and salt. Set aside.
In a large bowl, beat together the melted butter and sugar until creamy. Beat in the eggs one at a time, then stir in the vanilla. Gradually stir the dry ingredients into the wet mixture along with the milk. Spread the batter into the prepared baking pan.
In a small bowl, combine the pudding mix and chocolate chips. Sprinkle over the top of the cake batter.
Bake for 25 minutes in the preheated oven, until a toothpick inserted into the center of the cake comes out clean. Allow to cool before serving.
Interesting Facts
This cake is best served warm, with a scoop of ice cream or a dollop of whipped cream.
You can add different kinds of chopped nuts or dried fruit to the cake batter for extra flavor and texture.
This cake can also be made in a 9-inch round cake pan, or even a 9x13-inch pan.