Combine the herbs, scallions, ginger, garlic, fish sauce, and olive oil in a small bowl. Season with salt, pepper, and more fish sauce if you wish. Set aside.
Heat the broth in a large pot and add the leafy greens and half of the herb-ginger mixture. Bring to a simmer and season with salt and pepper. Simmer gently until the broth is very gingery and the greens have gone from perky and bright green to completely tender and dark green (looking more like braised than blanched greens), 15–20 minutes.
Meanwhile, cook the pasta in a pot of salted water until al dente; drain and add the pasta and chicken (if using) to the broth when it's ready, simmering for a few minutes to finish cooking. (Add the cooked rice here if going that route.)
Ladle the soup into bowls and top each with the remaining herb-ginger mixture. Squeeze with lots of lime or lemon.