In a small saucepan, combine the soy sauce, mirin, sake, sugar, and vegetable broth. Bring to a boil and then reduce heat to low to keep warm.
Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the tofu, mushrooms, onions, carrots, and celery and stir-fry for about 5 minutes, until vegetables are slightly softened.
Add the Napa cabbage and daikon radish and continue to stir-fry for another 3-4 minutes.
Drain and rinse the shirataki noodles and add them to the skillet.
Pour the warm sauce mixture over the vegetables and noodles and let it come to a simmer.
Reduce the heat to low and continue to cook for another 5-7 minutes, until the vegetables are tender and the sauce has thickened.
Serve hot, garnished with sliced green onions and sesame seeds if desired.