Preheat the oven to 400 degrees F (200 degrees C). Fit a piping bag with a coupler and large open star tip. Grease a baking sheet.
Fill a 3-quart pot with 4 inches water and 1 teaspoon salt. Add potatoes; bring to a boil. Reduce heat to low; simmer until tender, 20 to 25 minutes. Drain; return potatoes to the pot.
Cook potatoes over low heat until remaining water steams off, about 3 minutes. Cool at least 15 minutes.
Place potatoes in the bowl of a food processor; process until smooth. Let stand for 5 minutes. Add butter, egg yolks, remaining 1 teaspoon salt, nutmeg, and black pepper. Pulse until just combined; spoon into the piping bag. Gather bag edges and twist together.
Pipe potato mixture with a circular motion onto the prepared baking sheet into eighteen 2-inch rosettes; finish with a small peak in the center. Refrigerate until slightly firmer, about 25 minutes.
Beat 1 egg and heavy cream together in a bowl; brush onto rosettes.
Bake in the preheated oven until golden brown, 35 to 40 minutes.
