Preheat the oven to 400°. Place the potatoes in a large saucepan with enough salted cold water to cover by 1 inch. Bring to a boil, then simmer until the potatoes are tender, 12 to 15 minutes. Drain in a colander, then transfer to a bowl and mash thoroughly. Spread the mashed potatoes on a plate and set aside to cool.
Meanwhile, on a rimmed baking sheet, toss the bread cubes with the melted butter and salt to taste. Bake until the croutons are crisp and slightly browned, about 10 minutes.
In a large bowl, lightly beat the eggs. Add the cooled mashed potatoes, 1 cup flour, 1 1/2 teaspoons salt, the pepper and nutmeg; stir with a large wooden spoon until a heavy dough forms. If the dough is too wet to form into dumplings, add more flour, about 1/4 cup at a time; the dough should be slightly sticky.
On a work surface, cut the dumpling dough into 12 equal pieces. Press a crouton into a piece of dough and shape the dough into a ball around the crouton (wet your hands to prevent the dough from sticking). Repeat with the remaining dough and croutons.
5. Bring a large pot of salted water to a boil. Carefully drop the dumplings into the water and cook until they float to the surface, about 10 minutes. Remove and serve.