Add mushrooms. Toss occasionally and fry for 20-25 minutes until onion and mushrooms are caramelized. Reduce heat to medium-low if you feel they are browning too quickly.
Add water, increase heat to high and bring to a boil. Once the broth comes to a boil, reduce heat to low and simmer uncovered for 20 minutes.
While the broth is simmering, mix cooking sake, mirin, soy sauce, miso paste and tahini in a small bowl until smooth.
After the broth has simmered for 20 minutes, remove from heat and strain the broth, discarding the mushroom-onion mix. Return the liquid to the saucepan on low heat. Add the sauce mix to the pan, mix well and cook for 5-8 minutes until heated through. Remove and make your ramen.
Broth can be stored in the fridge for up to 4 days.