Whisk eggs and milk together. Season with salt, pepper and nutmeg. Spread butter on a flat, oven-safe dish. Add eggs and milk. Let it set in a water bath over low heat for approx. 20 minutes.
Heat the broth. Wash the chives, shake dry and cut into fine rings.
Punch the Eierstich onto a board. Cut out with a cookie cutter (stars, etc.).
Distribute the broth and egg custard on preheated plates, sprinkle with chives and serve.