In a large bowl, combine the ground turkey, breadcrumbs, spring onions, ginger, egg, lime zest, soy sauce, and black pepper. Using wet hands, shape the mixture into tablespoon-sized meatballs.
Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Cook the meatballs, turning several times until they appear browned on the outside. Set aside when browned, they do not have to be fully cooked yet.
Wash the taro, place in a pot and cover with water. Bring to a boil, reduce the heat and simmer about 10 minutes. Strain the taro and soak in cold water. When cooled, peel the skin off and rinse again. Cut the prepared taro into bite-sized pieces.
Heat the chicken stock in a large pot over medium high heat. When the water starts to boil, carefully add in taro pieces, carrots, soy sauce, and browned meatballs. Turn the heat down to low and simmer, stirring occasionally, for 20 minutes, until the vegetables are tender and the meatballs are cooked through.
When the cooking time comes to the last 5 minutes, heat 3 tablespoons of olive oil in a skillet over medium-high heat. Add the arugula and stir-fry, until just wilted. Stir it to the soup and season with salt and black pepper, to taste. Simmer for a couple minutes to allow the flavors to come together.
Remove from the heat and stir in springonions. Serve.