Move oven rack to middle position and preheat to 350 degrees F. Lightly spray a 9x13 pan with nonstick cooking spray, line bottom with a rectangle of parchment paper, and spray again with nonstick cooking spray.
In a medium bowl, whisk together flour, baking soda, baking powder, and salt; set aside.
In a stand mixer fitted with a paddle attachment, or with handheld beaters, beat butter on medium speed until smooth, about 2 minutes. Add sugar, and increase speed to medium-high. Beat until smooth and lighter in color, about 4 minutes. Scrape down sides of the bowl and add cocoa powder and vanilla and beat on medium for 1 minute. Add eggs and beat until combined, about 1 minute.
In a small saucepan bring water and milk just to a boil, and remove from heat.
Add flour and pulse mixer until no flour streaks remain. Carefully pour hot liquid into the batter, and pulse mixer until combined. Pour batter into prepared pan and smooth top into even layer.
Bake until cake begins to putt away from sides of pants and when a toothpick inserted in middle comes out clean, about 40-45 minutes. Move cake to wire rack and cool 20 minutes. Run a knife around edge of the pan, and place a wire rack on top of the cake pan. Use oven mitts to turn cake over onto wire rack, and remove parchment. Place a second wire rack on top of the cake, turn cake over once more so it’s now right-side up. Cool cake on a wire rack, about 2 hours.
7 MINUTE FROSTING:
In a medium saucepan over medium heat bring 1-inch water to simmer. In a medium bowl large enough to rest on sides of the saucepan, whisk together water, egg whites, sugar, cream of tartar and salt. Place bowl over barely simmering water, and using an electric hand mixer, beat mixture on medium-high speed until stiff peaks form, about 6-8 minutes.
Remove bowl from the saucepan, add vanilla, and continue to beat until mixture is cooled to room temperature and the icing is very thick and stiff about 8-10 minutes.
Immediately use offset icing spatula to frost cake. Sprinkle THE top of the cake with coconut (optional). Serve.