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For the cake: Preheat the oven to 325 degrees F. Spray the cake pans with nonstick cooking spray and line the bottoms with parchment. Whisk together the flour, cocoa powder, baking soda and salt in a large bowl until there are no lumps.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and granulated sugar on medium speed for 4 minutes. Add the eggs one at a time, beating until each egg is fully incorporated before adding the next one. When all the eggs have been added, increase the speed to medium-high and beat until light and fluffy, about 5 minutes
Turn the mixer to low speed and beat in half of the flour mixture until completely incorporated. Add the water or coffee and beat until completely incorporated. Add the remaining flour mixture and then the milk, beating after each addition until completely incorporated. Divide the batter between the cake pans and bake until a cake tester inserted in the center comes out with a few moist crumbs attached, 18 to 25 minutes. The cakes do not rise that much and will be very dense and fudgy.
Cool the cakes completely in the pans. Turn the cakes out of the pans, remove the parchment, and then chill them 2 hours or freeze 1 hour before assembling.
For the buttercream: Meanwhile, bring a pot of water to a simmer. Put the egg whites and granulated sugar in the bowl of stand mixer set over, not in, a saucepan of simmering water. Stir slowly until the mixture is warm and the sugar has dissolved. Put the bowl on the mixer fitted with the whisk attachment and whip on medium-high speed until cool. With the mixer running, add the butter in small additions. Add the espresso powder, vanilla extract and salt and whip until light and fluffy.
To assemble: Slice each cooled cake into 3 equal layers. Spread a thin layer of buttercream on top of 1 layer, top with another layer, and repeat with 3 more layers. Top with the last layer, and then frost the top and sides with the remaining buttercream. Refrigerate for at least 4 hours or freeze for 1 hour.
For the glaze: Put the chocolate in a small heatproof bowl. Bring the cream and corn syrup to a boil in a small saucepan, pour half over the chocolate and gently stir with a rubber spatula until smooth. Stir in the remaining cream mixture until the glaze is smooth and glossy. Buzz the glaze with an immersion blender, if you have one, to make it extra glossy.
Fill a disposable piping bag with the glaze; cut a small hole at the tip. Pipe the glaze around the top edge of the cake, working your way around in zigzag so the glaze dribbles over the edge. Pipe the remaining glaze over the top of the cakes to completely cover. Let the cake stand at room temperature to allow the buttercream to soften slightly, about 1 hour. Slice and serve.