Place the arame in a bowl and add water to cover. Let it soak 5 minutes to soften. Rinse and put in a small saucepan with the first tablespoon of tamari and about ½ cup of water. Cook on medium heat, about 10 minutes, until most of the water has evaporated. Drain and set aside.
Meanwhile, cook the lentils: Rinse, checking them over for little rocks masquerading as lentils. Put in a pot with water, bay leaf and the ¼ teaspoon of salt. The water should cover the lentils 2 inches. Simmer until tender, 20 minutes or so, until the lentils are tender to the bite—but not too soft. You want them to have some texture. Drain. Season with the first tablespoon of olive oil, some salt, and a generous grind of black pepper.
Chop the green and white parts of the onions—keeping them separate.
Heat the remaining olive oil in a wok or large heavy-bottomed skillet. And the white part of the onion, the garlic, and the ginger. Cook and stir about 5 minutes.
Stir in the butternut squash and the vegetable broth. Cover and cook 10 to 15 minutes, until the squash is just tender, adding more water if needed.
While the squash is cooking, bring a large pot of salted water to a boil. Add the soba noodles. Cook as directed on the package, until tender to the bite. Drain. Immediately place in a warm bowl, tossing with the sesame oil and remaining 2 tablespoons of tamari.
Gently toss the noodles with the reserved arame, the lentils and the squash. Season with more ground pepper and tamari, to taste.
Garnish with the chopped green onion and sesame seeds, if using. Serve immediately.