Put the broth into a pot over high heat and cover. When it begins to boil, add the shiitake, sweet peas, carrot, daikon radish, and ginger root. Reduce the heat and simmer, mostly covered, for 3 minutes.
Add the uncooked ramen noodles and zucchini to the pot. After about a minute the noodles will begin to unfold; gently separate them with a fork. Cook for a few more minutes or until the noodles are just tender.
In the meantime, ladle 1 cup of the broth into a small bowl. Add the miso paste, Sriracha, and coconut aminos. Whisk until smooth, then return to the pot; stir.
Stir in the lime juice.
Place a handful of arugula or spinach in each serving bowl. Ladle soup over top, then garnish with scallions.