Put the parsley, cilantro, and mint in a food processor and pulse until finely chopped.
Add the tahini, lemon juiceand 1 tablespoon water until smooth.
Continue blending, adding water 1 tablespoon at a time, until the desired consistency is reached (it should be thin enough to drizzle but not watery).
Set aside (can be made up to a few days ahead of time and refrigerated, but will thicken so bring to room temperature and stir in a little more water as needed before serving).
For the Middle Eastern Fish Cakes
Rinse out the food processor. Add the cilantro, parsley, mint, and pulse until finely chopped.
Add the 1/3 of the flounder/sole, lemon zest, ,za’atar and pulse until roughly chopped and combined (you want it to be well mixed but not a smooth paste).
Remove from the food processor and fold into remaining 2/3 pounds fish that has been chopped into ¼ inc dice
Form into 1½-inch patties.
Heat the vegetable oil in a large nonstick skillet over medium heat until shimmering. Add the patties, working in batches if necessary, and fry for 2 to 3 minutes per side, until lightly browned and cooked through.
Transfer to a paper towel-lined plate as they finish cooking.
Serve the fish cakes as a starter with the green tahini sauce drizzled over or on the side for dipping. To make it a full meal, serve with a couscous or freekeh and a simple salad of chopped tomato and cucumber.