In a large bowl, whisk together the flour and salt. In another bowl whisk together 2 cups water and eggs. Pour the liquid into the center of the flour mixture. Whisk until the smooth loose dough forms. Mix in parsley until well incorporated. Let rest for 15 minutes.
Place a large colander or strainer from a pasta pot over a pot of boiling water. You do not want the colander/strainer to touch the boiling water it should be suspended a couple of inches over the water. Add half of the dough to the colander and using a rubber spatula press the dough through the holes while holding it over the boiling water, allowing the dough fall through holes into the water. Let cook for two minutes then remove the dumplings with a slotted onto a sheet pan. Repeat with remaining dough (Reserve 2 cups of cooked dumplings for Round 2 Recipe German Dumpling Soup.)
In a large nonstick skillet over medium-high heat, add half the butter. When it is melted, add half of the dumplings to the skillet, season with salt and pepper to taste and cook until they are golden and slightly crispy in places, about 5 minutes. Repeat with remaining butter and dumplings. Transfer to platter and serve immediately.