In a medium or large bowl, mix in the eggs with the flour. It will be clumpy.
Slowly pour in about 1/4 cup of the milk at a time, mixing thoroughly to remove any clumpiness.
Then whisk in the water (you can also use milk for a richer taste). And lastly, add the salt, sugar, and oil.
Scoop out 1.5 cups of batter into a smaller bowl. Add cocoa powder to this mixture until well combined.
Add matcha powder to the remainder of the batter. Rest both for about an hour.
Heat a non-stick pan on medium heat (I use 6" pan). Once hot (test with a drop of batter and the bottom should cook within a few seconds), scoop just under a 1/4 cup of batter and spread on the pan. The crêpe should not be cooking too fast, slow enough you can spread out the batter, but fast enough it sets within 10 sec or so. Let it cook for 1-2 min before flipping over and cooking for another minute. The crêpe should naturally unstick from the pan. Repeat for remainder of both batters. They can stay in a stack as they cool to room temperature.
To make the whipped cream filling. Using a whisk (electric or by hand), whisk the cream until soft peaks form. Then add sugar and vanilla extract and continue whisking until stiff peaks form. Set aside until ready for use. Cover and refrigerate if needed.
To assemble, for this pattern, start with a chocolate layer. Spread a thin cream layer on top and repeat with 2 matcha layers. Continue this until all layers are used. The top layer will just be a crêpe. Sift the optional powders for garnish.