Heat oven to 400°. Using a fork, prick potatoes all over; place on a baking sheet. Bake until tender, 1 ½ hours; let cool, then peel and pass through a food mill or ricer.
Mix potatoes, butter, yolks, nutmeg, salt, and pepper in a bowl; transfer to a piping bag fitted with a ¾" star tip.
On a parchment paper-lined baking sheet, and working in a tight circular motion, pipe twelve 2 ½" cones about 2" high.
Brush with egg mixture; bake until golden brown, 40–45 minutes.
