In a medium bowl, beat the flour, eggs, and milk with a wooden spoon until smooth. Add the garlic, parsley, salt, and pepper. Stir well to develop some gluten. The mixture should be thick enough to spread on a cutting board without dripping, somewhat like a very thick pancake batter. If it’s too thin, add more flour. If it’s too thick, stir in more milk. Let stand 15 minutes.
Bring a large stockpot filled with water to a boil, add salt, and lower the heat to just under a simmer (few, if any, bubbles should appear on the bottom of the pan, and none should break the surface of the water). Set a saucepan on low with the butter.
Using a metal spatula or a long knife, spread some of the batter 1/4 inch thick on a small chopping board or the bottom of a cake pan or baking sheet. Shave off ribbons of batter about 3/8-inch wide into the water. The spaetzle will sink to the bottom.
When they float to the surface, after about 1 minute, they're done. If they don't float to the top, give them a nudge with a spider or a large, round slotted spoon. Skim the spaetzle from the water with the spider and let the water drain briefly, then deposit them into the saucepan with the melted butter.
Continue shaving off more batter into the water and cooking in batches until all the batter is cooked. Toss the spaetzle in the butter, season with salt and pepper if necessary, and serve. You can also turn up the heat on the saucepan to develop some browning on the spaetzle.