For the cake, preheat the oven to 350 degrees F. Butter three 9-inch round nonstick cake pans and line the bottoms with waxed paper.
Bring 2 cups of water to a boil in a medium saucepan over medium-high heat. Remove from the heat, add the cocoa powder and whisk until smooth. Allow to cool to room temperature, about 30 minutes.
Beat the butter in a large mixing bowl with an electric mixer on medium speed for 1 minute. Add the granulated sugar and beat until fluffy, about 2 minutes, scraping down the sides of the bowl occasionally. Add the eggs and vanilla extract and beat until well blended.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt. Alternately add the dry ingredients and the cooled cocoa mixture to the butter mixture in 3 additions. Beat until thoroughly mixed.
Divide the batter evenly among the prepared pans. Bake for 25 to 30 minutes or until a cake tester inserted in the centers of the cakes comes out clean. Transfer the pans to wire racks. Let cool in the pans for 10 minutes. Remove the cake layers from the pans and gently peel the waxed paper. Let cool completely.
For the filling, beat together the powdered sugar, butter and vanilla extract until smooth and spreadable. Set aside.
For the frosting, combine the chocolate chips, heavy cream and butter in a medium saucepan over medium-low heat, whisking until melted. Gradually add the powdered sugar and whisk thoroughly. Remove the pan from the heat and place in a large bowl that is partially filled with ice and cool for 5 to 10 minutes. Stir occasionally while cooling to prevent the frosting from becoming too stiff.
To assemble the cake, place a layer on a serving plate. (Use a serrated knife to trim the cake layers to a level surface if necessary.) Spread with half of the filling. Add the second layer and spread with the remaining filling. Top with the third cake layer. Spread the cooled frosting on the top and sides of the cake.
Serve immediately or cover the cake with a large bowl or cake keeper and refrigerate up to 3 days. Let the cake stand at room temperature for 30 minutes before serving.