In a large bowl whisk eggs, milk and squash. Gradually stir in enough flour to form a thick batter. Season heavily with nutmeg, salt and pepper. Using a rubber spatula, press batter through a colander into a large pot of boiling salted water. When spaetzle float to top, they are done. With a slotted spoon or spider transfer to a bowl filled with ice water, to cool. Drain and toss to lightly coat with oil. Set aside, refrigerated, for several hours, if desired or prepare immediately.

Melt butter in a sauté pan add spaetzle, and toss until warmed through; add parsley and bread crumbs, if desired and season to taste with salt and pepper.