Rub and rinse the dried mushrooms under running water for a couple minutes. Transfer to a small bowl and soak with tap water for at least 5 hours or overnight. Take out the soaked mushroom and keep the liquid (will be used later). Rinse mushrooms under running water and rub them all over. Remove the stems with scissors. Squeeze out as much water as possible. Pat dry with paper towels. Cut into ¼-inch strips. Transfer to a small bowl. Add salt, sugar, and corn starch. Mix well. Add the vegetable oil and mix again. Marinate for 30 minutes.
In a medium bowl, add pork, salt, sugar, soy sauce, and white pepper. Mix well. Add corn starch and sesame oil. Then mix again. Set aside to marinate for 30 minutes.
Place the rice cakes in a sieve. Rinse under running water and separate the rice cakes if they are stuck together. If you can't separate them, don't worry. It’s ok to have a few stuck together. Set aside to drain.
In a large nonstick skillet over medium-high heat, add 1½ tablespoons vegetable oil. Add shallot and cook for 1 minute. Add garlic and stir for another 30 seconds. Add green onion and cook for another minute. Push everything aside and add the pork. Sear for a minute without moving. Stir everything together. Add Shaoxing rice wine and cook for 1 minute. Toss in the mushroom and cabbage. Mix well. Pour in chicken broth and ¼ cup soaking mushroom liquid. Turn up the heat to high. Bring the mixture to a boil. Put the rice cakes in a single layer over the vegetables and pork. Cover with a lid and reduce the heat to medium-high. Cook for 3½ minutes.
In a small bowl, stir together the corn starch and cold water.
Remove the lid. Add the corn starch liquid. Stir fry for another 1 minute. Taste and adjust with soy sauce if needed. Transfer to serving plates and serve immediately.