Preheat the oven to 400 degrees F. Line two baking sheets with parchment paper.
Place the peeled potato chunks in a large sauce pot and cover with water. Add the salt and bring to a boil. Simmer the potatoes until fork-tender. Then drain off all the water and allow the potatoes to dry out a few minutes.
Place the potatoes back over medium heat. Add the shredded cheese, heavy cream, nutmeg, and white pepper. Use a potato masher or immersion blender to mash the potatoes into a fine smooth texture. Then quickly stir the egg yolks into the potato mixture.
Scoop the potatoes into a large piping bag fitted with a wide star tip. Pipe 1/2 cup mounds of potato onto the baking sheets, leaving room in between for the potatoes to expand.
Brush the tops of the Duchess Potatoes with melted butter. Bake for 20-25 minutes until golden on top. Garnish with fresh herbs if desired.
NOTE: Pipe the mounds high. They will spread and flatten a little as they bake.