In a small bowl, combine soju, tamari, mirin, and sesame oil. Set aside.
Bring water to a boil in a saucepan.
When boiling, turn off heat and add dried shiitake mushrooms. Soak 15 minutes, then drain, squeezing lightly to drain off extra water. (Alternatively you can keep the soaking water for another use like adding to soups, etc.)
Destem mushrooms and cut into 1/3-inch slices.
Heat skillet and add 2 teaspoons of the avocado oil.
Add mushrooms and cook over high heat, stirring occasionally until lightly browned in spots and tender, about 5 minutes.
Add all but 1 tablespoon of the soju mixture and cook, stirring, until mushrooms have absorbed the liquid, about 2 minutes. Transfer to a plate and set aside.
Rinse and wipe out skillet and heat remaining 1 teaspoon oil.
When hot but not smoking, add salmon pieces in one layer and cook over high heat, turning once, until lightly browned, about 5 minutes total.
Remove from heat and pour remaining soju mixture evenly on top.
Broil 2 inches from heat just until lightly glazed, 1-2 minutes.
Transfer to plate and top with mushrooms.
