Special equipment: a 10-inch nonstick skillet and 8-inch round cake pan
For the crepes: Whisk the eggs and flour in a medium bowl until smooth. Slowly whisk in the milk, 2 tablespoons warm water, 1/4 teaspoon salt and a few grinds of pepper until smooth. Refrigerate the batter, covered, at least 1 hour or overnight.
Heat a 10-inch nonstick skillet over medium heat, and brush with melted butter. Whisk the 2 tablespoons of melted butter into the crepe batter (batter will appear a bit grainy, but that's OK). Ladle a scant 1/4 cup batter into the skillet, and swirl the batter around to cover the bottom. Cook the crepe over medium heat until the top appears dry and the edge is starting to curl back, about 30 seconds. Flip the crepe with your fingers or a spatula, and cook until brown in spots, about 15 seconds. Transfer the crepe to a wire rack to cool. Repeat with the remaining batter, for a total of 12 crepes (you can stack them on the rack once they've cooled). (The crepes can be refrigerated, wrapped, overnight.)
For the cream cheese spread: Combine the cream cheese, capers, cornichons, dill, lemon juice and zest, 1/4 teaspoon salt and a few grinds of pepper in a medium bowl with a spatula. Drizzle in the heavy cream, and mix until smooth; set aside at room temperature.
To assemble: Line an 8-inch round cake pan with plastic wrap so it overhangs by 4 inches on both sides. Place 1 crepe (this will be the top of the cake, so pick a pretty one) on a work surface, and spread evenly with 2 tablespoons of the cream cheese spread. Transfer the crepe, cheese-side up, to the cake pan. Arrange pieces of gravlax evenly over the cheese spread, sprinkle with about 1 teaspoon of the lemon juice, then scatter with 1 tablespoon of the onion, followed by a generous tablespoon of the egg. Repeat 6 times. Spread the 8th crepe with 2 tablespoons of the cheese spread, then place it on top of the other layers, cheese-side down, to create the bottom of the cake. Stretch the plastic wrap over the cake to draw the lacy edges of the crepes up a bit and to cover the cake completely. Use a small cast-iron skillet or a large glass measuring cup to weigh down the cake and press it into an even shape. Refrigerate at least 1 hour up to overnight.
To garnish: Remove the weight from the cake, and peel back the plastic. Use the long sides of the plastic to ease the cake out of the pan. Flip the cake pan over, and set the crepe cake on top. Place a serving plate over the cake, and invert the cake onto it. Remove the plastic. Whip the cream in a medium bowl with a hand mixer on medium speed until stiff peaks form. Use an offset spatula to spread the whipped cream decoratively over the top of the crepe cake. Toss the dill, capers, cornichons and lemon zest in a small bowl until lightly combined, scatter the mixture over the whipped cream and sprinkle with salt and a few grinds of pepper.
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