Note: baking this cake at a slightly-lower-than usual temperature ensures that it bakes in a nice, flat layer, perfect for frosting.
Preheat the oven to 325°F. Grease a 9 x 13 pan (often called a brownie pan) with pan spray, line the bottom with parchment paper, and grease again.
Combine the flour, baking powder, baking soda, and salt in a medium bowl and set aside.
Simmer the water and prunes in a medium non-reactive pot for about five minutes at medium-high heat, or until the prunes are so soft you can easily squash them in half with a wooden spoon. Remove from the heat and let cool slightly before pureeing until very smooth (I use a magic bullet for smallish jobs like this as I abhor scraping small amounts from the bottom of a large blender).
Return the prune puree to the pot and add the butter and vanilla extract. Warm over low heat until the butter is melted, whisking the mixture until it is totally combined. Add the cocoa and continue to whisk over low heat until the cocoa has bloomed and suffused the mixture, and there’s no trace of dry cocoa.
Remove from the heat and add both sugars, whisking until smooth. Add the eggs and whisk until combined. Add the flour mixture and combine until no patches of dry flour remain. Finally, add the buttermilk and stir vigorously until it is fully incorporated.
Scrape the batter into the prepared pan and spread into an even layer, pushing the batter into the corner of the pans. Bake for 36-38 minutes, or until the edges of the cake have begun to shrink away from the sides of the pan, and a sharp knife inserted into the center comes out nearly clean, with perhaps a few stray crumbs. Allow to cool completely before frosting the cake.
For a simple presentation, you can halve the following buttercream recipe and serve the cake in the pan, with the buttercream swooshed attractively on top (this will give you just enough to ice the surface of the cake in a thin layer). Alternatively, you can read on and prepare a more highly decorated cake.
To make a two-layer sheet cake, allow your cake to cool completely and unmold it from the pan. Slice it neatly in half so that you have two 4 ½ by 6 ½ inch layers. Place the bottom layer on a cake stand or serving platter and dollop about a cup of buttercream on top, smoothing it into an even layer with an offset spatula. Chill briefly.
Place the second half on top and give your entire cake a quick crumb coat. Chill again for at least half an hour. When your crumb coat has chilled completely, frost the surfaces of your cake with an even, thin layer of buttercream.
If you have fun piping tips to play around with, this is a great opportunity to go wild with them - if you dont like how the cake is going, you can always scrape it off and start over!