Add flour, eggs, milk, water, and salt in a large bowl then mix with a hand mixer until you have a smooth, lump-free batter. At this point, mix in the butter or the vegetable oil. Alternatively, you can use them to grease the pan before frying each pancake. Heat a non-stick pan over medium heat, then pour in the batter, swirling the pan to help it spread. When the pancake starts pulling away a bit from the sides, and the top is no longer wet, flip it and cook shortly on the other side as well. Transfer to a plate. Cook the remaining batter until all used up. Serve warm, with the filling of your choice.