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1
Cook potatoes in large pot of generously salted boiling water until partially cooked (tester will meet some resistance), about 15 minutes. Drain potatoes, rinse in cold water, and drain again. Peel, cover, and chill until very cold, at least 4 hours and up to 1 day.
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2
Coarsely grate potatoes into large bowl. Melt butter in large ovenproof castiron skillet over medium-low heat. Add shallots; saute until soft, about 6 minutes. Add shallot mixture, 2 teaspoons coarse salt, and 1/2 teaspoon pepper to potatoes (reserve skillet). Toss to blend evenly (do not compact potato mixture). DO AHEAD:
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3
Let stand at room temperature.
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4
Preheat oven to 450u00b0F. Melt 4 tablespoons usli ghee in reserved skillet over medium heat. Add half of potato mixture (5 1/2 to 6 cups). Stir gently until ghee is absorbed, about 2 minutes. Spread potatoes to even layer, then press firmly with metal spatula to compact. Cook 5 minutes, pressing and flattening occasionally. Reduce heat to medium-low. Place slightly smaller skillet atop potato cake. Weigh down with heavy can (such as 28-ounce can of tomatoes). Cook potato cake 15 minutes, pressing occasionally.
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5
Remove can and small skillet. Press potato cake again to flatten. Spread with 2 tablespoons ghee.
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6
Place skillet in oven and bake potato cake uncovered 15 minutes. Run narrow spatula around potato cake. Turn out onto platter, bottom (crusty) side up. Immediately cut into wedges and serve with applesauce. Repeat with remaining potatoes and ghee.
