Heat olive oil in a large soup pot over medium heat. Add garlic, ginger, onion, carrot and celery and cook for 5 minutes stirring frequently.
Add 6 cups of water to the pot and bring to a gentle boil for 10 minutes.
Add broccoli, green beans, bok choy, and seaweed. Cook, stirring frequently, for 5-7 minutes. Remove from heat.
In a small bowl, mix the miso paste with about a 1/2 cup of hot water. Mix until it is completely dissolved in the water.
Add miso mixture, sesame oil, and green onions to the pot. Mix well and serve.