Make the tahini dressing by blending all dressing ingredients together in a food processor or blender until smooth.
In a large bowl or on a large serving platter, add the lettuce, broccoli, red cabbage, carrots, green peas, chickpeas, pistachios, and strawberries, then top with sliced grapefruit and garnish with Parmesan cheese. Serve with strawberry tahini dressing.