Method:
For the falafel, add water to falafel mix according to package instructions. Stir in parsley and onion. Let sit for 10 minutes.
Roll tablespoons of the mixture into balls. Heat vegetable oil in a skillet to a depth of about 1/4 inch. Heat until oil sizzles when a drop of water hits its surface. Add falafel and brown on all sides, 4 to 6 minutes, turning occasionally.
Alternatively, to bake the falafel, preheat oven to 400°F. Oil a baking sheet and set falafel balls on it. Brush them with oil and bake for 8 to 10 minutes. Turn them and bake 8 to 10 minutes longer, until browned.
Meanwhile, make the tahini yogurt sauce by whisking together yogurt, tahini, garlic, lemon juice, salt and pepper. Thin with water to obtain a smooth sauce.
Serve warm falafel with sauce, warm pita bread, lettuce, tomato and cucumber.