In a large bowl, whisk together the flour, eggs, milk (or water), and salt. Stir until the mixture is smooth and slightly sticky. Let the dough rest for 5-10 minutes.
Bring a large pot of salted water to a boil. Using a Spaetzle maker or colander, press small amounts of dough into the boiling water. Cook the Spaetzle for 2-3 minutes, or until they float to the surface. Remove them with a slotted spoon.
In a large frying pan, melt the butter over medium heat. Add the cooked Spaetzle and sauté for 3-4 minutes, or until golden and slightly crispy on the edges.
Serve the Spaetzle immediately as a side dish or toss with cheese for Käsespätzle.