Carefully, cut top off each hard-boiled egg with an egg cutter or sharp serrated knife. Use a small spoon to completely scoop out the eggs, keeping separate the contents of the first four eggs. Discard the contents of the others. Reserve the shells. Chop the whites and yolks of the four eggs. In a food processor, cut up the shallots finely. Add the chopped eggs, sour cream, vodka, and a small pinch of cayenne pepper. Mix thoroughly in a food processor. Use a spoon to add half of the caviar. Season to taste with salt and pepper, remembering that caviar is already salted. With a small spoon, fill each eggshell with the egg and caviar mixture and top with a small amount of the remaining caviar. Place eggs on a tray filled with kosher salt to prevent them from tipping over. Refrigerate until ready to serve. Eggs can be eaten with a small spoon, strips of toasted bread, or Belgian endive leaves cut in half lengthwise so that they can fit inside the egg.