Cook butter over medium heat in a medium fry pan until melted. Continue to cook until the butter turns golden brown then gently pour the brown butter into a small bowl and set aside until cool.
In a blender, combine milk, and salt and pulse 2-3 times until combined. Add flour and blend for 30 seconds until extremely smooth. Then add the brown butter and pulse again until combined and smooth. Transfer to a large bowl and let rest in the fridge covered for between 10 minutes and up to 24 hours. The consistency you are looking for is that of heavy cream (not pancake batter)
To cook the crêpes, heat a 10 inch crêpe pan over medium-high heat till a drop of water sizzles. Using a piece of paper towel, wipe 1/4 teaspoon butter on the base of the pan. Pour 1/4 cup of batter into the centre of the pan and working extremely quickly tilt and turn the pan until the batter spreads evenly across the bottom in a thin circle. Cook till the edges begin to dry and lift from the pan and the bottom is browned, then flip with a spatula or your fingers and cook until the second side is browned.
Transfer crêpe to a large plate and repeat with remaining batter, adjusting the heat and adding more butter to the pan for every three crêpes. Stack completed crêpes on top of each other when finished. They will soften as they cool.
It is likely that your first crêpe will be a disaster, this is normal so don’t worry. You can make the crêpes from three days in advance or even longer and freeze them.
To assemble - In a small bowl combine crème fraîche, dill and lime zest and juice.
Start with a crêpe and add a thin spread of crème fraîche and a layer of smoked salmon. Top with another crêpe and then add a more generous spread of crème fraîche. Top with another crêpe and alternate between a crème fraîche and salmon layer and just a crème fraîche layer until you have 5 salmon layers and 10 crêpe layers.
You can leave the crêpe cake rustic, or take a knife and cut off the rough edges so you can see the layers. To serve, top with the salmon caviar and some fresh dill sprigs.
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