In a large mixing bowl or blender, combine eggs, flour, milk, water, melted butter, vanilla extract (if using), and salt.
Whisk thoroughly or blend for about 30 seconds until the batter becomes smooth and lump-free.
Cover the batter and refrigerate for at least 1 hour or up to 4 hours.
Heat an 8-inch nonstick skillet or crepe pan over medium heat.
Lightly brush the pan with butter.
Pour about 3 tablespoons of batter into the center of the pan.
Immediately tilt and rotate the pan to evenly coat the bottom with a thin layer.
Cook for 30 to 45 seconds, until the underside is lightly browned.
Carefully flip the crepe using a spatula.
Cook the second side for 10 to 15 seconds until lightly browned.
Transfer the cooked crepe to a large plate and cover with a clean kitchen towel to keep warm.
Repeat the process with the remaining batter, lightly greasing the pan with butter between each crepe as needed.
Serve warm with fresh fruit, Nutella, whipped cream, or a dusting of powdered sugar.