Combine flour, eggs, baking soda, salt and milk in a larger bowl. Mix the batter with a spatula for a few minutes, then turn on the hand mixer. Continue mixing with the hand mixer, slowly adding water as necessary. (You may need more or less water.) Mix until the batter is free of crumbs, and is completely smooth with a consistency (thickness) of heavy cream.
Pour oil into a small bowl. Take a paper towel and dip it in the oil, and then use the paper towel to coat the crepe pan with it. Heat up the pan on the highest until it's really hot.
Transfer a small amount of batter into the pan by using a ladle. Watching that the batter doesn't leave the pan, swirl it around until the batter coats the pan bottom evenly. When the crepe has slightly browned on the bottom (about 30 seconds), flip it around to the other side. Place the finished crepe on a plate.
Oil the pan with a paper towel. Heat the pan again, then repeat the process until you are out of batter.