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1
Mix the eggs and milk in high-speed blender or food processor to combine. Add the flour, cocoa, sugar, vanilla, salt and brown butter and blend for about 5 seconds, or until the batter is completely smooth. Pour into a container, cover, and refrigerate for at least 1 hour or up to 2 days.
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2
When you are ready to cook, if the ingredients have separated, gently stir the batter.
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3
Cut about 15 sheets of parchment paper into 8- to 10-inch squares and pile on a plate beside the stove top. Place an 8- to 10-inch crepe pan or nonstick skillet with sloped sides over medium heat. (If you have two crepe pans, using both will make the process go faster.) Place the small saucepan of melted skimmed butter near the pans, with a pastry brush nearby.
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4
When the pan is hot, brush it with a very thin, light coating of the skimmed butter and heat for 15 to 20 seconds. Add about 21/2 to 3 tablespoons of batter and swirl the pan to coat-if there is any excess, dump it out into a small bowl. If you notice how much you need for each crepe as you go, you will get better and better at adding the right amount of batter to the pan. (Note that you might have to discard [read: eat] your first crepe; that's typical when you make crepes.)
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5
Cook for about 1 minute, until the edges of the crepe begin to dry. Using your fingers or an offset spatula, turn the crepe over and continue cooking for about 10 to 15 seconds more; transfer to a plate and place a sheet of the pre-cut parchment paper on top. Repeat the process: grease the pan with the melted, skimmed butter, and use all of the batter, stacking each crepe on top of the last, separated by a sheet of parchment paper, as you go. (You can make crepes with the leftover batter that you poured out of the pan into the small bowl, but they will likely become chef's treats; that batter has been heated a bit and might cook up a bit differently.) You will end up with 15 to 16 crepes (don't worry; this cake is very forgiving). At this point, you can proceed to the filling assembly of the cake or freeze the crepes (see Kitchen Tips).
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6
Make the filling: In a food processor, pulse the cookies 5 to 10 times, about 1 second per pulse, until they become fine crumbs. Pour them out into a large bowl; you should have about 13/4 cups. Wipe the processor bowl and blade clean. Combine the mascarpone, cream cheese, sugar, and vanilla in a the processor. Process for 20 to 40 seconds, until completely smooth, stopping to scrape the bowl down about after about 10 to 15 seconds. Transfer the cheese mixture into the bowl with the cookie crumbs and stir gently to combine. Do not overmix or you will lose the fun speckled look.
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7
Make the crepe cake: Place one crepe on a serving platter. Coat with about 3 tablespoons filling, smoothing it gently with a spatula to 1/2 inch of the edge. Place another crepe on top, spread the surface with filling, and repeat with the remaining crepes and filling until the stack reaches at least 4 inches in height. You can build it as tall as you like (see Kitchen Tip).
