In a 6-quart kettle, bring 5 quarts salted water to a boil.
In a large bowl whisk together flour and salt.
In a heavy saucepan, bring milk just to a simmer. Put the parsley in a blender. With the blender motor running, add the milk to the parsley, and blend until milk is very green.
In a bowl, whisk together eggs and water and add green milk in a slow stream, whisking constantly.
Add milk mixture to flour mixture, whisking until mixture forms a soft, smooth batter-like dough.
Force the dough through a spaetzle-maker into the boiling water, or drizzle through a large-holed colander.
Stir the spaetzle gently, to separate, and boil for 5 minutes, or until just tender.
In a large colander drain the spaetzle and place in serving bowl.
In a small heavy saucepan, cook the rosemary with salt and pepper, to taste, in butter over moderate heat, stirring, for 2 minutes.
Drizzle the rosemary butter over the spaetzle, tossing well.
Season the spaetzle with salt and pepper.