Mix the milk with the eggs, water, and vanilla extract in a measuring cup.
Mix the sifted flour with salt and sugar in a mixing bowl. Make a well in the center.
Gradually pour the milk mixture into the center while whisking in a circular motion, starting from the center. Occasionally tap the edge of the bowl to make the flour fall to the center and obtain a smooth, homogeneous batter.
Once all the milk is incorporated and you have a smooth batter, add the melted butter, hot but not scalding. Mix well.
Note: If you still have lumps, pass the batter through a fine sieve.
Take 250 g / 8.8 oz of plain batter and gradually add it to the unsweetened cocoa powder, mixing after each addition to avoid lumps.
Pour the cocoa batter into a sauce bottle or a cleaned ketchup bottle. Cover both batters and let them rest for 1 to 2 hours before cooking.
After the resting time, heat a frying pan over medium heat and grease it with a little butter using a paper towel or a brush. Mix the batter before using it.
Remove the pan from the heat and hold the bottle of cocoa batter above it. Create a spiral starting from the center to the edge of the pan.
Return the pan to the heat. The batter cooks almost immediately. If there are areas with raw batter, wait until they're dry before pouring the plain batter.
Pour a small ladle of plain batter, tilting the pan to spread it evenly and cover the entire surface uniformly. Pour just enough batter to cover the bottom to get thin crepes.
As soon as the edges start to lift slightly, flip the crepe. If you want them to stay white without browning, remove them quickly from the heat. I browned mine a bit too much.
Stack the crepes on top of each other and cover them with a clean kitchen towel to keep them warm and soft.
Spread a little of your chosen spread, slightly fold the two edges, then roll the crepe to form a roll.
Enjoy the soft swirl crepes cold, warm, or hot according to your taste.
If you want to enjoy them the next day and reheat them, preheat the oven to 150°C (302°F), then turn it off before placing the crepes in a dish. Leave them for about ten minutes. You can also reheat them in a hot pan, with the heat off, covering them.