Wash and dry the potatoes. Arrange them on a bed of rock salt in a shallow baking pan and bake until done, 30 to 35 minutes.
Remove the potatoes from the oven and cut them into halves. (Reserve the hot rock salt.) Scoop out the pulp with a melon-ball cutter or small spoon, being careful to keep the shells intact. Mash the pulp slightly in a small bowl and keep warm.
Pour oil to a depth of 3 inches into a large saucepan and heat to 375°F on a deep-frying thermometer. Drop the potato shells into the oil and fry until golden brown and crisp, 1 to 2 minutes. Drain well on paper towels.
Fill the potato shells with the mashed potatoes, top with a spoonful of sour cream, and add ¼ teaspoon or more of caviar. Serve as a first course atop the hot rock salt on thick salad plates.