Chocolate Cake with Cream Filling

2 cups boiling water
1 cup unsweetened cocoa powder
2 3/4 cups all-purpose flour
2 teaspoons baking soda
1/2 teaspoon baking powder
1/2 teaspoon salt
1 cup butter
2 1/2 cups sugar
1/2 teaspoon vanilla extract
4 eggs
1 cup very cold heavy cream
1/4 cup confectioners' sugar
1 teaspoon vanilla extract
1/2 cup butter, softened
3 1/2 cups confectioners' sugar
1/4 cup cocoa powder
1/3 cup heavy cream
1 teaspoon vanilla extract

Preheat oven to 350 degrees. Grease and flour 3 9-inch cake pans.
Place the 1 cup cocoa powder in a medium bowl and pour the boiling water over it. Stir with a fork until smooth and set aside to cool.
In a medium bowl, combine flour, baking soda, baking powder, and salt. Whisk to mix well.
In the large mixing bowl of an electric mixer, beat butter and sugar on high speed until smooth.
Add vanilla and eggs, one at a time, beating well after each addition and scraping down the sides of the bowl if necessary.
Add flour mixture in 4 batches, beating just until combined.
Add the cocoa mixture in 3 additions, stopping to scrape down the sides of the bowl. Once the batter is smooth, turn the mixer off and divide evenly between the 3 prepared pans.
Place in oven and bake for 25 to 30 minutes or until the top of cake springs back when lightly touched.
Place cake pans on a wire rack and lets cakes cool in pans for 10 minutes. Remove cakes from pans and place back on a wire rack to cool completely.
To make the filling, place heavy cream, confectioners' sugar, and vanilla in a medium bowl and beat with an electric mixer until thick. Refrigerate until needed.
To make frosting, place butter in the bowl of an electric mixer and beat until smooth. Add 1 cup of confectioners' sugar and beat until combined. Add half of the cream with the mixer on low and then remaining ingredients, including what is left of cream. Turn mixer to high and beat until smooth.
Spread whipped cream between the cake layers and frosting on sides and top of the cake. Store leftovers in the refrigerator.