Udon with Mushroom Broth, Cabbage, and Yams

Using tongs, remove kombu and mushrooms; discard kombu.

Transfer mushrooms to work surface; cut off stems and discard.

Cut each mushroom into 3 to 4 strips.

Strain broth through fine-mesh strainer into another large pot; discard solids in strainer.

Add tamari and rice vinegar to broth.

DO AHEAD: Can be made 1 day ahead.

Cover and chill mushrooms.

Cool, cover, and chill broth.

Bring large pot of salted water to boil.

Cook yams until just tender, 4 to 5 minutes.

Using skimmer, transfer to medium bowl.

Cook snow peas, cabbage, and carrots separately until crisp-tender (snow peas, 30 seconds; cabbage, 1 1/2 minutes; carrots, 2 minutes).

Using skimmer, transfer vegetables to separate bowls.

Reserve cooking liquid.

DO AHEAD: Vegetables can be cooked 2 hours ahead.

Let vegetables and liquid stand at room temperature.

Bring cooking liquid to boil.

Sprinkle with salt.

Add noodles; cook until tender but still firm to bite, stirring often.

Drain; rinse.

Meanwhile, bring vegetable broth to simmer.

Add green onions and ginger strips.

Season with salt and pepper.

Using tongs, divide noodles among bowls.

Divide mushrooms, yams, snow peas, cabbage, and carrots among bowls, each in separate mound.

Divide tofu, if using, among bowls.

Ladle broth over and serve, passing sambal oelek and tamari separately.