Start by making the filling for the eggplant. Place the shrimp in a food processor along with the ground pork, salt, sugar, white pepper, sesame oil, 1 tablespoon vegetable oil, and rice wine. Process until a rough paste forms. Transfer to a bowl, and stir in the egg, cornstarch, and half of the chopped scallions. Set the mixture aside in the refrigerator for 30 minutes.
Cut each eggplant into 1 1/2-inches thick slices on the diagonal. Take each slice and carefully slice through the middle, but don’t cut all the way through. The pieces should still be attached on one side. This will help keep both halves of the eggplant together.
Fill the middle of each eggplant slice with the shrimp and pork filling. Once all the slices are stuffed, heat a tablespoon of oil in a skillet over medium-high heat, and fry the slices on both sides until golden. Add a little more oil whenever the pan starts to look a little dry (you’ll only need a tablespoon at a time).
Remove from the pan and place on a heatproof plate for steaming. Prepare your steamer with 2-3 cups water (you can also use a wok with a steaming rack placed in the bottom). Heat until the water is simmering. Turn off the heat, carefully place the plate in the steamer. Cover the steamer and turn the heat back on to medium-high. Steam for 7-10 minutes. The eggplant should be very soft. Nothing worse than an under-cooked eggplant!
While the eggplant is steaming, make the sauce. Heat a saucepan over medium heat, and add 1 teaspoon oil, sesame oil, and minced garlic. Cook for 30 seconds, and then add the chicken stock, oyster sauce, soy sauce, and sugar. Season with salt and pepper to taste. Bring the sauce to a simmer, and stir in half of the cornstarch slurry. Cook for a minute to thicken. Set aside.
After the eggplant is done, pour any liquid left on the plate into the sauce. Heat the sauce and add more cornstarch slurry if it needs thickening. Stir in your reserved scallions, pour over the eggplant, and serve.