In a large pot, combine 6 cups of the water and split peas and bring to a boil.
Reduce heat and simmer, covered, for 1 hour. Stir occasionally so they don't stick on the bottom.
Add the vegetables and simmer another 30-45 minutes, until the peas are very soft (depends on the age of the peas).
Meanwhile, whisk together the remaining 1 cup of water with the tahini and the remaining engredients. If your tahini is quite thick, do this in the food processor or blender, much easier. Stir the tahini mixture into the soup and serve.