In a large pot or Dutch oven, heat the olive oil (3 tablespoons). Sauté the green onions, celery, and garlic over medium-low heat until very soft and only just starting to brown, about 3 minutes.
Add the zucchini and kosher salt (1 teaspoon). Stir to coat. Pour in the broth (3 cups). Cover and simmer on low until zucchini is very tender, about 10 minutes. Turn off the heat. Stir in the fresh dill (2 tablespoons), lemon zest, and lemon juice.
Using an immersion blender directly in the pot (or a standing blender in batches, carefully), puree the soup until very smooth (see notes). Whisk in the Greek yogurt (1 cup)(unless freezing or making ahead- see notes).
Serve, topped with more yogurt, a swirl of olive oil, and extra dill/green onions, if desired.
When adding the Greek yogurt, be sure to turn off the heat. The yogurt can separate when the soup is boiling or too hot, so it's best to add the yogurt just before eating when the soup is warmed up already. If reheating soup with Greek yogurt already in it, just try not to bring it to a boil. If freezing, I recommend freezing the soup before adding the yogurt - it will freeze beautifully without - and then after defrosting and heating up, whisking in the yogurt as directed. And if it separates a little, all is not lost - it will still taste delicious!
An immersion blender blends the soup right in the pot, meaning fewer dishes - yay! A standing blender will do a better job at pureeing the soup, though. Personally, I don't think using a blender is worth the extra dishes for a slightly smoother texture. Feel free to do what you want here.
I used a HUGE ZUCCHINI from my garden - it was three pounds! With large zucchinis like this, there are often large tough seeds. I scooped out my seeds but left the skin on and it worked perfectly in this blended soup. With smaller zucchini, you don't need to worry about taking out any seeds.