Place potatoes in a large pot and cover with salted water; bring to a boil. Reduce the heat to medium-low and simmer until just tender, 15 to 20 minutes. Drain and let cool until easily handled.

While the potatoes are cooling, melt butter in a skillet over medium heat. Add bread cubes; cook and stir until golden brown and crunchy, 4 to 5 minutes. Remove from the heat and use a slotted spoon to transfer croutons to a bowl. Reserve browned butter in the pan.

Peel potatoes and place into a large bowl. Mash and season with nutmeg, cayenne, salt, and pepper. Add eggs and mash until combined. Stir in flour just until incorporated; do not overmix.

Bring a pot of salted water to a simmer. Dampen your hands with water and scoop a spoonful of dough onto your palm. Shape dough into a circle, make a light indentation in the center, and place 2 or 3 croutons inside. Pull dough around croutons to seal and roll into a smooth ball. Repeat to make seven more dumplings.

Use a large spoon to lower dumplings, one at a time, into the simmering water. Cook until they float to the top, 1 to 2 minutes. Cover and simmer over medium-low heat for 10 minutes. Flip dumplings and continue to cook until puffed and cooked through, about 10 minutes more.