Peel 2 potatoes and ½ carrot and cut them into bitesize pieces.
Soak the potatoes in a bowl of cold water for 5 minutes to remove excess starch.
While you wait, boil a small pot of water and blanch 10 snow peas for 1 minute. After one minute, drain and set aside for later. Once cool enough to touch, cut them in half. Note: this step is mainly for presentation so you can sprinkle them on top at the end. Alternatively, you can add the snow peas later, directly to the pot of dashi in the final minute of cooking.
Drain the potatoes and rinse them with cold water. Place them in a heatproof bowl along with the carrots and add 1 tbsp water. Cover with plastic wrap and microwave at 600W for about 3 minutes as a shortcut for parboiling. (Alternatively, boil or steam until parboiled.)
Pour 500 ml dashi stock into a large pot, add the parboiled potatoes, carrots and 100 g shimeji mushrooms, and bring to a boil. Check the carrots and potatoes frequently to ensure they don't overcook.
In the meantime, heat a frying pan over medium and add 1 tsp cooking oil. Sprinkle 2 salmon fillets (or double the amount of mini fillets) with salt on both sides, then place skin-side down and fry until nicely browned (approx 3 minutes on each side), then remove from the heat and set aside.
Once the potato and carrots are cooked to your liking, turn off the heat. Place 2 tbsp yellow miso paste (awase) on a mesh spoon or ladle and dip it into the broth, whisking to incorporate it into the dashi and break any lumps.
Divide the soup into serving bowls and place half a salmon fillet (or whole mini fillet), 5 snow peas and a small square of butter on top of each serving. Sprinkle with ground black pepper to taste. Enjoy!