In a small bowl, combine the shiitakes with 1 tablespoon of tamari, the sesame oil, mirin, and ¼ teaspoon salt. Toss to coat and set aside to marinate for 10-20 minutes.
In a medium bowl, combine the olive oil, remaining tablespoon of tamari, the garlic, and ¼ teaspoon salt. Place the salmon in the marinade and turn to coat. Let marinate while you prepare the dressing.
Make the dressing: In a blender, combine the tahini, tamari, mirin, rice vinegar, sesame oil, maple syrup, garlic, ginger, and sambal oelek. Blend for 15–30 seconds to combine. With the blender running on low speed, slowly drizzle in the olive oil until the dressing is thickened and homogenous.
Transfer the dressing to a liquid measuring cup or medium bowl and stir in the sesame seeds, scallions, and salt. Set aside.
Arrange the salmon, shiitakes, sweet potato, and egg in the steamer insert, leaving a space for the broccoli.
Fill the multi-pot halfway with water, then set the colander insert inside. Cover and bring to a boil. Once boiling, season the water well with salt. Add the soba noodles to the colander insert. Fit the steamer basket insert into the colander insert and cover with a lid. Steam for 4 minutes, then remove the lid and add the broccoli florets to the steamer insert. Cover again and cook for another 4 minutes, until the salmon is opaque and cooked through, the sweet potatoes are tender, and the broccoli is bright green.
Remove the pot from heat. Uncover the pot and carefully remove the steamer insert, using the handles provided. Remove the colander insert with the soba noodles and allow the water to drain from the colander.
Immediately run cold water over the soba noodles and egg to halt the cooking, then let cool completely. Drain the noodles well to remove any residual moisture.
Peel the egg and cut in half.
Toss the cooled noodles in a medium bowl with ¾ cup (80 ml) of the dressing, reserving the remaining dressing for serving.
Divide the noodles between 2 bowls and top each bowl with half of the salmon, shiitakes, sweet potatoes, broccoli, egg, cabbage, and pickled radish. Drizzle with the remaining dressing, then top with the sesame seeds and scallions.