Add 2 tablespoons of butter and the oil to a large skillet over medium heat. Add the cooked spaetzle and saute until slightly browned, about 2 to 3 minutes. Remove from the pan to a serving platter and set aside while you cook the mushrooms. Set the skillet back over high heat and add a little more olive oil and remaining 2 tablespoons of butter. Add the thyme, mushrooms and garlic and saute until golden brown, about 4 to 5 minutes. Season with salt and pepper, to taste. Add the cream and mustard and stir well. Reduce the mixture until the sauce is nice and thick, about 3 minutes. Fold in the spaetzle. Transfer to a serving bowl, garnish with chives and serve alongside the pork schnitzel, if desired.
In a large bowl, combine the flour, salt, pepper, and nutmeg. In another mixing bowl, whisk the eggs and milk together. Make a well in the center of the dry ingredients and pour in the egg-milk mixture. Gradually draw in the flour from the sides and combine well; the dough should be smooth and thick. Let the dough rest for 10 to 15 minutes.
Bring 3 quarts of salted water to a boil in a large pot, over medium heat. Reduce the heat to a simmer. To form the spaetzle, hold a large holed colander or slotted spoon over the simmering water and push the dough through the holes with a spatula or spoon. Do this in batches so you don't overcrowd the pot. Cook for 3 to 4 minutes or until the spaetzle floats to the surface, stirring gently to prevent sticking. Drain the spaetzle in a colander and give it a quick rinse with cool water. This can be made up to 1 hour in advance.