Drain soaked shiitake mushrooms (reserve the soaking water), remove stems and chop into small cubes. Set aside.
Peel turnip. Then cut into two halves. Grate one half and cut the other half into small strips.
In a skillet, add turnip strips and a little bit of water and cook over low-medium heat, stirring occasionally so the turnip does not brown, for about 6 minutes or until turnip becomes translucent. Add more water as needed.
Add grated turnip and reserved mushroom water to skillet. Cook for 5-6 minutes. Reserve any cooking liquid left. Set aside and let cool.
Heat up sesame oil in a clean skillet over medium-high heat and fry mushrooms until fragrant, about 3 minutes. Add soy sauce and fry for 2-3 more minutes. Set aside.
Pour the cooking liquid from turnip into a measuring cup, and add water to make up to 200ml.
In a big mixing bowl, add cooked turnip, mushrooms, water, rice flour, salt, sugar, and white pepper. Mix until combined. Add more water if you prefer a softer cake texture.
Pour batter into an oiled container. Steam over medium-high heat for 50 minutes or until an inserted stick comes out clean.
You may slice it up now and eat it as is, or you may pan-fry it.