Put a kettle or medium saucepan of water on high heat and bring it to a boil for the rice noodles.

Set a large soup pot on the stove over medium heat and add the sesame oil.

Add the scallion whites to the soup pot. Cook for 1 minute, stirring often, until they start to soften.

Add the grated ginger to the soup pot. Stir for about 30 seconds, just until it smells fragrant.

Add the sliced mushrooms to the soup pot. Cook for 4 to 5 minutes, stirring now and then, until they shrink and pick up some browned spots.

Add the broccolini to the soup pot. Cook for 2 minutes, stirring, until it turns bright green.

Pour the vegetable broth and 2 tablespoons of the soy sauce into the soup pot. Raise the heat to high and bring the broth to a gentle boil.

Add the tofu cubes to the soup pot. Lower the heat to medium-low and let the soup simmer for 3 minutes so the tofu heats through.

When the water is boiling, add the rice noodles to the medium saucepan. Cook them according to the package directions, usually 3 to 4 minutes, until tender but not mushy.

Drain the noodles in a colander. Rinse them briefly under warm water and let them drain well so they do not stick together.

Add the drained noodles to the soup pot. Stir gently and cook for 1 minute, just until the noodles are hot in the broth.