Cake: Heat oven to 375 degrees F. Line a jellyroll pan with wax paper; grease.
Sift flour, cocoa, baking powder and salt together twice; set aside.
Place eggs in small mixing bowl. Beat with electric mixer 5 minutes or until
thick and lemon-colored. Slowly beat in sugar, 1 tablespoon at a time. Mixture
will become very thick. Transfer to large mixing bowl. Beat in water and vanilla
extract. Slowly add flour mixture; beat until smooth. Pour into prepared pan,
spreading evenly to corners.
Bake for 12 to 15 minutes, or until cake tests done.
Loosen from pan. Turn out on rack; remove wax paper. Invert; cool completely.
Filling: Combine baking chocolate, broken into pieces, and cream in heavy
saucepan. Heat slowly; stirring constantly, until chocolate melts. Transfer
to medium-size mixing bowl. Stir in rum; chill for 1 to 2 hours.
Beat with electric mixer until stiff and thick.
Cut cake in half crosswise. Place 1 piece of cake on small cookie sheet.
Top with chocolate filling; spread to form even layer 1 1/2 inches thick. Top
with remaining cake layer. Chill at least 1 hour.
Prepare icing. Combine corn syrup, water and butter in small saucepan. Bring
to boil; cook until butter melts. Remove from heat.
Add chocolate bits; stir until chocolate melts. Cool at room temperature.
Spread over top of cake. Chill until frosting sets.
Cut cake into 12 squares; arrange on decorative plate.