Step 1

Combine mushrooms, kombu, and 2½ cups cold water in a 1-qt. jar or small bowl. Cover and chill until dashi takes on a light golden hue, at least 8 hours or overnight.

Step 2

Strain dashi into a clean jar or bowl. Squeeze mushrooms to release excess liquid into jar, then remove and discard the woody stems; thinly slice mushroom caps and reserve. Discard kombu.

Step 3

Do Ahead: Dashi can be made 2 days ahead; cover and chill. Cover and chill rehydrated mushrooms separately.

Step 4

Cook noodles in a medium saucepan of boiling salted water according to package directions. Drain in a colander, shaking off excess water, and set aside.

Step 5

Pour dashi into a 1.5–2-qt. donabe or small saucepan and stir in mirin and soy sauce; season with salt. Bring to a simmer over medium heat. Add squash and turnips, cover, and cook until vegetables are almost completely tender, 5–7 minutes. Uncover; add greens, tofu, white and pale green parts of scallions, and reserved mushrooms. Cover and cook until greens are wilted, tofu is warmed through, and squash and turnips are tender, about 2 minutes.

Step 6

Add reserved noodles to donabe and top with scallion greens. Drizzle with oil and sprinkle with shichimi togarashi.