Place the flour in a mixing bowl, make a well in the center, and break the eggs into it. Add the salt, vanilla sugar, and either the powdered vanilla or the zest. Pour in a bit of milk.
Whisk well and continue gradually adding the rest of the milk while stirring from the center outward. The batter should be very smooth.
You can blend the batter with an immersion blender if you still have lumps. If using butter, melt and add hot after mixing well. Add it a little at a time.
Leave the batter to rest for an hour. It will thicken slightly; thin it out with water for very light crepes.
Lightly grease your pan with a paper towel coated with a little oil, or use softened butter to grease the pan.
Pour a small ladle of batter into the pan and swirl to cover the entire bottom. Flip the crepe over to the other side as soon as it loosens and the edges are golden brown.
Cook the crepe on one side and flip it over. Lightly brown the other side and remove.
Place on a plate and stack the crepes on top of each other as you cook them. They'll stay warm and soft.