In a large bowl, sift flour. Whisk in eggs and salt. Gradually add the water (around 1 cup) until the dough develops. It should be sticky to touch and just thin enough to be pushed through spätzle maker or a large holed colander with spoon.
Bring water with salt to a simmer. Place a spaetzle press or large holed colander over the pot and fill with batter. Slide the press back and forth or use a wooden spoon to press the batter through the holes of the colander to create the dumplings. Stir gently to remove any pieces from the bottom of the pot. Cook until they float to the top, remove with a strainer, and drain.
Clean the mushrooms and cut into slices. Peel the onion and dice.
In a large skillet, melt butter over medium heat and add the onions. Add the mushrooms and toss well. Season with salt and pepper, simmer for 5 minutes and remove with a slotted spoon to a plate.
Sprinkle flour into the skillet. Stir in broth and cream. Simmer for about 5 minutes until it thickens. Stir in the mushrooms and season if needed. Cook until just heated through. Toss with the spätzle on serving plate. Sprinkle with parsley and serve immediately.