Cake: In medium bowl, combine cocoa with boiling water, mixing with wire whisk until smooth. Cool completely. Sift flour with soda, salt, and baking powder. Preheat oven to 350 degrees. Grease well and lightly flour three 9-by-1 1/2-inch layer-cake pans.
In large bowl of electric mixer, at high speed, beat butter, sugar, eggs, and vanilla, scraping bowl occasionally, until light -- about 5 minutes. At low speed, beat in flour mixture (in fourths), alternately with cocoa mixture (in thirds), beginning and ending with flour mixture. Do not overbeat.
Divide evenly into pans; smooth top. Bake 25 to 30 minutes, or until surface springs back when gently pressed with fingertip. Cool in pans 10 minutes. Carefully loosen sides with spatula; remove from pans; cool on racks.
Frosting: In medium saucepan, combine chocolate pieces, cream, butter; stir over medium heat until smooth. Remove from heat. With whisk, blend in 2 1/2 cups confectioners' sugar. In bowl set over ice, beat until it holds shape.
Filling: Whip cream with sugar and vanilla; refrigerate.
To assemble cake: On plate, place a layer, top side down; spread with half of cream. Place second layer, top side down; spread with rest of cream. Place third layer, top side up.
To frost: With spatula, frost sides first, covering whipped cream; use rest of frosting on top, swirling decoratively. Refrigerate at least 1 hour before serving. To cut, use a thin-edged sharp knife; slice with a sawing motion.
Serves 10 to 15.