Puree the carrots with the milk in a blender. Put the milk and carrot mixture in a bowl and add the remaining ingredients except for the salted water, mix everything well.
Let it soak for approx. 10 minutes and pour it into boiling salted water using a spaetzle slicer or a spaetzle press. Let the spaetzle steep until they float on the water, then pour into a sieve and drain well.