In a 6-quart soup pot, place the vegetables, dill, and parsley. Cover with water or vegetable broth and simmer for 30 minutes until tender.
Remove from heat. Drain and reserve the broth.
Puree with an immersible blender using enough of the reserved broth to get a smooth puree. (Or place in a blender and mix on low until pureed.)
Cook orzo according to package directions while soup cooks. Drain
Place the vegetable puree and orzo in a large pot. Stir to combine. Thin with a little broth or water, if necessary. Simmer for 2-3 minutes, until warm.
Remove soup from heat.
Thin tahini with the salted water and lemon juice until smooth and pourable. Slowly pour into the soup, mixing thoroughly. Taste and adjust seasonings, if needed.
For an authentic Greek meal, serve with Stuffed Zucchini with Avgolemono Sauce