Step 1In a small bowl, soak the red dates in cold water until softened, about 30 minutes. When softened, remove and discard the pits.
Step 2Meanwhile, cut each candy slab into 8 pieces. Place the candy in a heatproof bowl and pour 2 cups boiling water over the candy. Set aside until the candy is dissolved and completely cooled.
Step 3Grease a heatproof, 8-inch-round, 3- to 4-inch-deep soufflé dish or other straight-sided bowl, using 2 teaspoons vegetable oil.
Step 4Place the rice flour in a large bowl. Make a well and stir in the cooled sugar water. Knead the mixture until a dough forms in the bowl, adding an additional 1/3 cup cold water until the dough is smooth, slightly moist and shiny, 5 to 10 minutes.
Step 5Place the dough into the prepared dish and pat until it fills the dish evenly and the top is level.
Step 6Halve the red dates and place, cut-side down, in a ring around the outside of the dough, leaving a few to decorate the center.
Step 7Sprinkle the top with sesame seeds. Coat with the remaining 1 teaspoon oil, using your fingers and lightly pressing down on the dates and sesame seeds.
Step 8In a covered steamer large enough to fit the dish without touching the sides of the steamer, bring water to a boil over high heat. Carefully place the dish in the steamer, cover, and steam until the cake begins to pull away from the sides of the pan, 35 to 45 minutes. Check the water level occasionally and replenish, as needed, with boiling water.
Step 9Carefully remove the dish from the steamer and pour off any excess liquid on the surface. Place on a rack to cool. Loosely cover and set at room temperature in a cool room until the next day, when it will be ready to eat.
Step 10Run a knife along the edge of the cake to loosen the sides. Place a cake rack over the bowl and invert to unmold. Flip the cake right-side up on a cutting board. Wrap the cake in plastic and refrigerate until ready to use.
Step 11When ready to eat, cut the cake into quarters. Cut each quarter crosswise into two (2-inch-wide) strips. Cut each strip crosswise into scant 1/4-inch-thick slices. Beat the egg in a small bowl, until frothy. Dip the slices in the egg.
Step 12Heat a flat-bottomed wok or skillet over medium heat until hot but not smoking. Add just enough vegetable oil to barely coat the wok. Pan fry the egg-dipped slices in batches until golden brown, 2 to 3 minutes on each side. Serve immediately.