For the salad: Heat 1/4 inch of oil in a skillet over medium-high heat until shimmering. Fry the pita pieces until lightly browned, 30 to 60 seconds on each side. Transfer to a paper towel and immediately sprinkle lightly with salt.
In a large bowl, combine the pita chips with the spinach, mint, tomatoes, radishes, cucumber and onions. Season with a few turns of black pepper and salt to taste.
For the tahini dressing: Whisk together the tahini, lemon juice, sumac, salt, garlic and 1/4 cup water, stirring until thickened. Drizzle half of the dressing over the salad and toss. Serve with the remaining dressing on the side.