PREP PAN: LINE one half sheet pan with a Silpat mat. Spray with Pam (with flour) or Baker's Joy. Note: I like to use Silpat mats because they lie very flat, unlike parchment paper, which wrinkles when sprayed with non-stick spray.
PRE-HEAT OVEN TO 325° F (165° C).
SIFT flour, cocoa, and baking soda. Add instant coffee and salt and whisk to blend.
MIX eggs and egg yolk on low speed in Kitchen Aid (or other stand mixer), using the whisk, until combined. Gradually drizzle in the sugar with mixer running; turn speed to high and continue to whip until thick and pale in color, about 10 minutes.
TURN speed to low and add mayonnaise, a spoonful at a time, with mixer running. Add vanilla.
ADD 1/3 of the flour and pulse in gently on lowest speed.
ADD 1/2 of the water and mix in.
REPEAT with another 1/3 of the flour and 1/2 of the water.
FINISH by adding the remaining 1/3 of the flour and mix just until all the flour is incorporated.
STOP the mixer and scrape down sides and bottom of bowl and mix in. The batter will be very thin.
POUR into the pan and spread batter evenly with an offset spatula.
BAKE @ 325° F (165° C) about 25 minutes, until a wooden skewer tests clean, and the cake is just starting to pull away from the sides of the pans.
LET COOL in the pan.
FREEZE cake in the pan, overnight if possible. Freezing the cake makes it easier to cut.
INVERT frozen sheet cake and spread the melted chocolate in a thin layer on the bottom of cake. Although this is an optional step, it is a professional technique that gives a nice finish to the layers, especially the bottom layer of a cake. I almost always do this when when working with sheet cakes.
CUT the cake into desired rounds or other shapes, depending on what you are using it for.