In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 5 minutes until translucent.
Stir in the minced garlic and grated ginger, cooking for an additional minute until fragrant.
Pour in the vegetable broth and water, bringing the mixture to a gentle boil.
Add the sliced mushrooms, chopped bok choy, and julienned carrot. Reduce heat and let simmer for 10 minutes until the vegetables are tender.
In a small bowl, whisk together the miso paste and soy sauce with a few tablespoons of the hot broth until smooth. Stir this mixture back into the pot.
Gently add the cubed tofu and sesame oil, cooking for another 5 minutes to heat through.
Serve hot, garnished with sliced green onions and sesame seeds if desired.