Beat eggs with a whisk.
Add water and salt to eggs.
Stir in the flour 1 cup first, then adding additional flour if needed, until mixture forms a ball. [Note: Do not add too much flour. Add enough flour where the mixture is gooey but holds together. ]
Bring the water (or soup) to a rolling boil and add a small teaspoonful of dumpling mixture to the boiling liquid. The water (or soup) must be boiling as each spoonful of the mixture is added to it. Do not let the liquid stop boiling as you are adding the dumplings to the pot. If it stops boiling, let it resume boiling before adding more spoonfuls. [Tip: To keep the batter from sticking to the spoon as you are adding it to the boiling water, dip the spoon and scraper in the boiling liquid each time. This will make each spoonful slide into the liquid smoothly.]
When all the dumplings are in the water (or soup), turn the heat down to medium and boil uncovered for 5 minutes.
Cook for 10 minutes or longer, until done. The dumplings will rise to the top. You may test one by breaking it in half and if the center is formed and looks dry-ish, it is done.
Note: If cooked in boiling water (e.g., not in a soup), drain the water when cooked and serve the dumplings immediately [Tip: Egg dumplings are great with melted brown butter (e.g., heat butter until it browns) and then pour butter over dumplings and serve with jelly or applesauce.]