Blend flour, salt, pepper, and nutmeg in large bowl. Whisk in eggs and milk, forming soft batter. Mix in half of herbs.

Bring large pot of salted water to boil. Butter large bowl. Working with 1/3 cup batter at a time and using rubber spatula, press batter directly into boiling water through 1/4-inch holes on coarse grater, strainer, or wide ladle. Stir spaetzle to separate and boil 2 minutes. Using fine sieve, scoop spaetzle from pot, drain well, and transfer to buttered bowl. (Can be prepared 3 hours ahead. Let stand at room temperature.)

Melt 2 tablespoons butter with 1 tablespoon oil in heavy large skillet over medium heat. Add mushrooms; sauté until beginning to soften, about 4 minutes. Add onion; sauté until beginning to soften, about 5 minutes. Add remaining 2 tablespoons butter, 1 tablespoon oil, and spaetzle. Sauté until spaetzle begin to brown, stirring often, about 10 minutes. Add 3/4 cup broth. Simmer until broth is absorbed, adding more broth if dry. Mix in remaining herbs; season with salt and pepper.