Fry salt pork with onion in a skillet until the salt pork is golden brown, about 10 minutes. Drain fat and set salt pork and onion mixture aside.
Mix mashed potatoes, egg, salt, black pepper, and nutmeg together in a bowl; stir 1 cup flour into potato mixture. Sprinkle 1 cup flour onto a work surface and turn the dough out onto the flour. Knead the flour on the work surface into the dough.
Cut dough into 12 equal pieces and roll into balls, dusting your hands and sprinkling work surface with remaining 1/2 cup flour. Press your thumb into each dumpling to make an indentation, and fill with a small amount of salt pork-onion mixture. Pinch the dumplings closed and roll in flour.
Bring water to a boil in a large pot. If desired, replace half the water with beef broth. Drop dumplings into the boiling water and broth and reduce heat to low. Simmer until cooked through, about 25 minutes. Drain and transfer to a serving bowl.