Using a wooden spoon, mix flour, eggs, salt and enough water to make a thick viscous batter. Let stand for 20 minutes. (The batter should not be too thin, but must form bubbles when being beaten with the spoon).
Meanwhile, bring a pot of salted water to the boil. Heat butter in a pan and brown onions in hot butter.
When the water is boiling, form spaetzle directly over the boiling water using a spaetzle-maker. Allow water to come to the boil again and remove spatzle as soon as they float. Repeat with remaining batter.
Place spaetzle into a preheated bowl and toss with the onions and cheese. Serve immediately.
If you don't have one, you can press the batter through the holes of a colander.