The mystery of why this cake is called a pie remains unsolved, but there's no doubt that the custard-filled layer cake topped with a dark chocolate glaze reigns as a favorite dessert.
Heat oven to 375°F. Grease 2 straight-sided 8-inch round baking pans. Line bottoms with waxed paper; grease paper.
Mix flour, powder, salt in a bowl. Beat butter, sugar, milk, egg, vanilla in large bowl on medium 2 minutes. Add flour mixture all at once; beat 2 minutes, until smooth (few lumps may remain). Divide among pans.
Bake in 375°F oven 25 to 30 minutes, until toothpick tests clean. Cool in pans on racks 10 minutes. Unmold cakes; remove paper. Cool.
Mix sugar, flour, salt in small saucepan. Stir in milk. Cook over medium heat, stirring, until thickened, 10 to 15 minutes; cook 2 more minutes, stirring. Remove from heat.
Using a fork, beat yolks slightly in small bowl. Stir in about 1/2 cup hot milk mixture. Stir yolk mixture into milk mixture in pan; cook over low heat, stirring, 1 minute (do not overcook or eggs will begin to set up). Remove from heat. Stir in vanilla. Place plastic wrap directly on surface. Let cool.
Invert cake layer on platter. Stir cooled filling; spread over top of layer. Invert second layer on top.
Melt butter and chocolate in saucepan over low, stirring. Scrape into bowl. Add sugar; beat just until mixed. Stir in water; beat until smooth. Let stand until good coating consistency, 10 minutes. Slowly pour over top, spreading, allowing some to flow over edge.