How to Make It
Preheat oven to 375°F. Pierce potatoes all over with a fork, and place on a parchment paper–lined baking sheet. Bake at 375°F until tender, about 1 hour. Let stand on baking sheet at room temperature until cool enough to handle, about 15 minutes.
Meanwhile, fold an 8-inch square piece of cheesecloth into quarters to make a 4-layer, 4-inch square. Using medium holes of a box grater, grate ginger; place in center of cheesecloth. Gather edges of cheesecloth, and squeeze over a bowl to equal 1 tablespoon ginger juice. Discard solids.
Increase oven temperature to 400°F. Cut potatoes in half length-wise; carefully scoop potato pulp into a medium bowl, leaving about 1/4 inch pulp around shell. Return 12 potato shells to baking sheet; discard remaining 4 shells. Add ginger juice, milk, and butter to pulp in bowl, and mash with a potato masher until smooth; stir in 1 1/2 teaspoons salt, nutmeg, and pepper. Spoon mashed potato mixture evenly into 12 potato shells (about 1/2 cup per shell).
Beat egg whites, cream of tartar, and remaining 1/8 teaspoon salt with a mixer on high speed until foamy, about 20 to 30 seconds. Add powdered sugar, 1 tablespoon at a time, beating at high speed until stiff peaks form, about 2 minutes. Stop mixer; scrape sides of bowl. Spoon meringue evenly onto potatoes on baking sheet. Bake at 400°F until meringue is golden brown, 6 to 7 minutes. Transfer to a platter; serve immediately.