Melt 3 tablespoons of butter in the microwave or a small saucepan. Set it aside to cool for about 5 minutes. It should be liquid, but not hot enough to cook the eggs.
Add the cooled melted butter, flour, sugar, salt, milk, water, eggs, and vanilla extract to a blender.
Secure the lid and blend on medium-high speed for 20-30 seconds, or until the batter is completely smooth with no lumps. The final consistency should be similar to heavy cream.
Pour the batter into a bowl, cover it with plastic wrap, and let it rest in the refrigerator for at least 30-60 minutes, or up to 24 hours.
Before you start, give the chilled batter a quick stir to recombine any ingredients that may have separated. Set up your station with the bowl of batter, a ladle or ¼ cup measure, your reserved butter for greasing, and a plate for the finished crepes.
Place an 8-inch non-stick skillet over medium heat. Let it get properly hot. A good test is to add a tiny drop of water; it should sizzle and evaporate immediately.
Add about ¼ teaspoon of butter to the hot pan and swirl it around to coat the bottom.
Pour about 3-4 tablespoons of batter into the center of the pan. Immediately pick up the pan and tilt and swirl it in a circular motion to spread the batter into a thin, even layer that covers the bottom. The first crepe is often a “test crepe,” so don’t worry if it’s not perfect!
Cook for 1-2 minutes. You’ll know it’s ready to flip when the edges begin to dry and lift away from the pan, and the surface looks matte and no longer wet.
Use a thin spatula to gently lift one edge of the crepe. If it releases easily, slide the spatula underneath and flip it over. Cook for another 30-60 seconds on the other side. It doesn’t need to brown much on the second side.
Slide the finished crepe onto a plate. Repeat the process with the remaining batter, adding a small amount of butter to the pan between each crepe to prevent sticking.