In bowl, sift together first 5 ingredients. Stir in milk and shortening. Blend in chopped nuts.
Spread into a 9x9-inch pan. Sprinkle with mixture of brown sugar and 1/4 cup cocoa. Pour water over the entire batter. Bake at 350 degrees for 45 minutes.
During baking, the cake mixture rises to the top and chocolate sauce settles to bottom. Invert squares of pudding on dessert plates. Dip sauce from pan over each. Alternatively, the entire pudding can be inverted on to a deep serving patter. Serve warm with or without whipped cream.