For The Filling, Place The Sugar, Cornstarch, And Salt In A Small Heavy Saucepan, And Stir To Combine.
Gradually Whisk In The Milk.
Fold In The Chocolate, And Place The Pan Over Medium-High Heat, Stirring Constantly Until The Mixture Bubbles Up And Thickens, 8 To 10 Minutes.
Remove The Pan From The Heat, And Stir In The Vanilla.
Let The Filling Cool To Room Temperature, Then Place In A Glass Bowl, Cover With Plastic Wrap, And Chill Until Ready To Assemble The Cake.
For The Cake, Place A Rack In The Center Of The Oven, And Preheat The Oven To 350°F.
Grease And Flour Two 9″ Cake Pans, Shake Out The Excess Flour, And Set The Pans Aside.
Place The Cocoa In A Medium-Size Bowl.
Pour Some Of The Milk—About ½ Cup—Into The Cocoa, And Stir To Make A Paste.
Whisk In The Remaining Milk Until The Mixture Is Smooth.
Set Aside.
In A Large Mixing Bowl, Combine The Butter, Shortening, And Sugar, And Blend With An Electric Mixer On Medium Speed Until Light And Creamed, 1 Minute.
Add The Eggs And Vanilla And Blend On Medium-High Until Smooth And Fluffy, 1 Minute More.
Sift Together The Flour, Baking Powder, And Salt In A Small Bowl.
Add These Dry Ingredients To The Batter Alternately With The Cocoa, Beginning And Ending With The Dry Ingredients.
Beat Until Just Combined.
Scrape Down The Sides Of The Bowl With A Rubber Spatula And Stir The Batter Until Smooth.
Divide The Batter Between The 2 Pans, And Place The Pans In The Oven.
Bake Until The Cake Just Pulls Away From The Sides Of The Pans, 30 To 35 Minutes.
Remove The Pans To A Wire Rack To Cool 10 Minutes.
Run A Knife Around The Edges Of The Pan, Give The Pans A Gentle Shake, And Invert Them Once And Then Again To Cool Completely Right Side Up, About 45 Minutes.
Meanwhile, Make The Frosting.
Place The Chocolate In The Top Pan Insert Of A Double Boiler.
Place This Pan Over An Inch Of Boiling Water In The Bottom Of The Double Boiler Over Medium Heat.
Whisk Until The Chocolate Melts.
Remove The Pan Insert, And Whisk In The Butter, A Little At A Time.
Place Back Over The Simmering Water If Needed To Melt The Butter.
Whisk In The Hot Water, Corn Syrup, And Vanilla.
Place The Pan Insert In A Large Mixing Bowl Filled With Ice.
Beat With An Electric Mixer On Medium-High Speed Until The Frosting Is Thickened And Spreadable, 5 To 8 Minutes.
Set The Frosting Aside.
To Assemble The Cake, Slice The Cake Layers In Half Crosswise Using A Long Serrated Knife.
You Will Have 4 Layers.
Crumble 1 Layer With Your Fingers Into Crumbs That Will Cover The Cake.
Place These In A Small Bowl And Set Aside.
Remove The Filling From The Refrigerator.
Place 1 Cake Layer On A Cake Platter And Spread Half Of The Filling Over The Top Of It, Spreading To ½” From The Edge.
Place A Second Layer On Top, And Repeat With The Remaining Filling.
Place On The Top Layer.
If Needed, Insert 5 Or 6 Long Toothpicks Down Into The Cake From The Top To Stabilize It.
Place The Cake In The Refrigerator To Chill For 15 Minutes.
Remove The Cake From The Refrigerator, And Frost The Top And Sides Of The Cake With Smooth Strokes.
Press The Cake Crumbs Onto The Sides Of The Cake First, Then Pile The Remaining Crumbs On Top Of The Cake.
Slice And Serve.
