Adjust oven racks to the upper middle and lower middle positions and preheat oven to 400 degrees. Line 2 rimmed baking sheets with parchment paper.
In a Dutch oven or large stockpot, add potatoes and 1 tablespoon salt. Add cold water to cover potatoes by 1 inch.
Over medium-high heat, bring to boil and partially cover pot. Cook until potatoes are tender when pierced with a paring knife, stirring once or twice, about 10 to 15 minutes. Drain well, tossing in colander to remove excess water.
Wipe pot dry. Return potatoes to pot and mash until very smooth. Using a rubber spatula, fold in egg yolks one at a time, making sure each yolk is completely incorporated before adding the next.
Stir in the butter, cream, nutmeg, and salt and pepper (I like 1 teaspoon salt and ½ teaspoon pepper) until the mixture is smooth.
Transfer to a large piping bag fitted with a 1/2-inch star piping tip and pipe 12 round mounds (2 ½ inches wide by 2 inches tall) onto each prepared baking sheet, spacing them about 2 inches apart. Sprinkle with the cheese.
Place both sheets in the oven and bake for 15 minutes. Rotate the pans top to bottom and front to back and continue baking until the tops of the potatoes are light golden brown, about 10 minutes longer. Garnish with minced fresh parsley if desired.
