1
In a container or zip-top bag, combine the miso paste, sugar and sake until fully dissolved. Add the salmon and marinate for 4-12 hours.
2
Place the carrots, chiles and radishes in a heatproof bowl. In a saucepan, bring the rice wine vinegar, sugar, salt and ginger to a boil, stirring to dissolve. Pour the pickling liquid over the vegetables, let cool, and store in the fridge for as long as you're marinating the fish.
3
In a large pot, combine the dashi powder, kombu and 4 cups of water. Bring to a boil, then turn off the heat and remove the kombu. Whisk in the ginger, miso paste and soy sauce and return to a boil. Turn off the heat and let the broth sit for 1 hour. Strain.
4
Preheat the oven to 375°F.
5
In a bowl, combine the soy sauce and balsamic vinegar. Add the shiitake mushrooms and marinate for 10 minutes.
6
Bring a large pot of salted water to a boil. Add the noodles and cook according to package instructions. Drain the noodles, return to the pot, and drizzle with canola oil to prevent sticking.
7
Remove the salmon from the marinade and sprinkle with salt. Place on a baking sheet, along with the mushrooms and bok choy. Toss the bok choy with the canola oil and a pinch of salt.
8
Roast everything for 12-15 minutes, until the salmon is cooked through and the vegetables are tender. Season the vegetables with salt and pepper.
9
Divide the noodles between bowls. Ladle in dashi broth and top with salmon, mushrooms, bok choy and pickles.