In a large bowl, whisk together flour, nutmeg, and parsley; season with salt and pepper. In another bowl, whisk the milk, eggs, and five tablespoons oil until smooth, then whisk milk mixture into the flour mixture until combined.
Bring the water to a boil in a large pot; add salt. Working in batches, pass batter through a potato ricer fitted with a 1/8-inch-hole blade into the water (or push through large holes of a colander with a rubber spatula). Cook until spaetzle float to the top, about 30 seconds. Use a slotted spoon to transfer them to a colander. Repeat until all batter is used.
Heat remaining two tablespoons oil in a large nonstick skillet over medium-high heat. Add beans, saute until just tender. Add spaetzle, season with salt and pepper, and cook until heated through. Serve immediately; garnish with parsley.