Heat the olive oil in a large Dutch oven or soup pot over medium heat.
Add the sliced carrots and celery. Cook for 5 to 6 minutes, stirring occasionally, until they begin to soften.
Add the green onions, garlic, and fresh ginger. Cook for about 1 minute, just until fragrant.
Stir in the toasted sesame oil, 3 tablespoons of tamari, the cooked chicken, chicken broth, and cilantro.
Bring the soup to a boil over high heat. Then reduce the heat and let it simmer gently for 15 to 20 minutes so the flavors can blend. Taste and add more tamari, sesame oil, or cilantro if needed.
While the soup simmers, place the rice noodles in a bowl and cover them with hot water. Let them soak for 15 to 20 minutes until softened. Drain the water.
Add the softened noodles to the soup and cook for about 5 more minutes so they finish softening. Serve warm