Cut the stale rolls into small cubes no bigger than 1/2 inch (1.25 centimeters) wide. Place them in a large bowl.
Pour the hot milk over the cubed rolls. Set aside and allow to soak for 30 minutes.
Melt the butter over medium low heat in a large pan. Add the onion and Speck.
Cook, stirring often, until the onions are just softened and translucent, but not browned. Remove from the pan and set aside to cool.
Once the onions and Speck have cooled, add to the bowl with the bread. Add the eggs, flour, parsley, salt, and nutmeg.
Mix together the ingredients with your hands until well combined.
Allow the mixture to rest at room temperature for 15 minutes, then divide into 10 equal pieces.
Lightly moisten hands with water and form each piece into a compact ball. Each ball should be about 2.5- 3 inches (6-8 centimeters) wide.
Bring a large pot of salted water to a boil. Reduce heat to a low simmer and add the Speckknödel in batches. Cook until floating to the top and heated through, about 15 minutes. Use a slotted spoon to gently remove the dumplings from the water.
Serve immediately in hot beef broth with fresh chives.