Add the flour and salt to the bowl of a stand mixer. Stir to combine. Crack the eggs into a small bowl and whisk them. Make a well in the center of the flour mixture and pour the eggs in it. Add the milk (start with using slightly less and add more as needed). Attach a dough hook to the stand mixer and "knead" the dough for 16-20 minutes, or until bubbles appear (see pictured instructions for details). After 15 minutes or less of beating, use a wooden spoon to scoop and pull the dough. If bubbles/holes appear, the dough is done.
Bring at least 2 quarts of lightly salted water to a boil, then reduce to a simmer. Using a Spätzle maker of your choice (I use and prefer the Spätzle press), press the noodles into the simmering water and cook for about 2-3 minutes, or until the noodles float to the top. Use a slotted spoon to transfer the noodles to a colander, and then dump the noodles in a large bowl of ice water. Drain the noodles again, toss with some melted butter and serve warm.
Make Ahead: The Spaetzle can be stored in the fridge for at least a couple of days and then reheated. Melt some butter in a large skillet and toss the Spätzle in it to heat through.
Traditionally Spätzle batter is quite thick because it was cut into noodles using the board & knife method. Even if using a Spätzle press or other method, thicker batter yields a better consistency. If you're using the Spätzle press yes, it will require some muscle strength - you don't want the batter to be so runny that it squishes right through with ease. That said, if you're straining way too hard to press the batter through, go ahead and add a bit more liquid to thin it out.