For the Croutons/Crumbs:
1 stick unsalted butter
2 cups fresh bread cubes
salt and freshly ground black pepper to taste
1 pinch cayenne pepper, or to taste
1 pinch freshly grated nutmeg, or to taste
2 large eggs
1 cup all-purpose flour
1 tablespoon snipped fresh chives, or to taste
Place potatoes in a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until just tender, 15 to 20 minutes. Drain and let cool until easily handled. Meanwhile, 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 heat and transfer bread to a bowl using a slotted spoon. Reserve the browned butter in the pan. Peel potatoes and place them in a large bowl. Mash and season with salt, pepper, cayenne, and nutmeg. Stir in eggs and mash until combined. Add flour; stir just until flour disappears. Do not overmix dough. Bring a pot of salted water to a simmer. Dampen hands with water and scoop a spoonful of the dough onto your palm. Shape into a circle, make a light indentation in the center, and place 2 or 3 croutons inside. Roll into a smooth ball, sealing in the croutons. Repeat with remaining dough and croutons. Use a large spoon to lower dumplings into the simmering water, one at a time. Cook until they float to the top, 1 to 2 minutes. Cover and simmer over medium-low heat until set, flipping dumplings over halfway, until 20 minutes. Place dumplings on a serving plate. Drizzle with reserved browned butter. Crumble remaining croutons on top and garnish with chives. Let dumplings firm up slightly before serving, about 10 minutes.