Whisk the flour, sugar, and salt in a large bowl.
Dig a well in the center. Add the eggs and the milk.
Whisk from the center outwards, slowly incorporating the flour until you have a smooth, thick paste.
Slowly pour in the cold water, melted butter, and vanilla while whisking until the batter is smooth and runny (like heavy cream).
Let the batter sit at room temperature for 30 minutes.
Set pan to Medium-High. The pan needs to be hot enough to sizzle the moment batter hits it.
Lightly butter the pan, then wipe it almost completely dry with a paper towel.
Pour approx. ¼ cup of batter. Immediately lift and swirl to coat the bottom thinly.
Cook ~45–60 seconds until edges lift and spots appear. Flip and cook ~15–20 seconds just to set the other side.
As each crêpe finishes, pile them on a plate.
IMMEDIATELY cover the stack with a clean kitchen towel or pot lid.
If the batter thickens up while it sits, whisk in a splash of cold water to loosen it back up.