Bring water to a boil in a medium pot. Add dashi packs and simmer for a few minutes, then remove the packs. (You can skip this step if you use prepared dashi liquid.)
Cut zucchini into 1-inch pieces, then slice each piece lengthwise into 6 wedges.
Slice onion into thin strips. (3-5mm thick)
Add zucchini and onion to the simmering broth. Bring to a boil again, then cook for 1–2 minutes over medium heat until the vegetables are tender. Skim off any foam for a smoother taste (optional), then remove from heat.
Place miso in a ladle and dissolve it with chopsticks or a small whisk. Gradually mix into the soup, making sure not to boil after adding miso.
Garnish with chopped green onions if desired and serve immediately.