Prep the leeks well: Slice the leeks lengthwise, fan out the layers, and rinse thoroughly to remove grit. Thinly slice the white and light green parts.
Sweat the aromatics: Warm olive oil in a large pot over medium heat.
Add leeks, carrots, and celery with a pinch of salt. Cook 6–8 minutes, stirring, until the leeks are soft and glossy but not browned.
Add garlic and herbs: Stir in garlic, thyme, and the bay leaf. Cook 30–60 seconds until fragrant.
Broth in, then simmer: Pour in vegetable broth.
Bring to a gentle boil, then reduce to a simmer for 8–10 minutes to let the flavors meld.
Cook the orzo: Stir in the orzo and simmer 8–10 minutes, stirring occasionally so it doesn’t stick to the bottom. Cook until the pasta is just tender.
Finish with lemon and greens: Stir in lemon zest and juice. Add spinach or kale and cook 1–2 minutes, just until wilted.
Season with salt and pepper to taste.
Serve: Ladle into bowls and top with fresh parsley or dill. Add grated cheese if you like a salty, savory finish.