Preheat oven to 425°F (220°C) with a rack in the center. Line a large rimmed baking sheet with parchment. In a small bowl, whisk the smoked paprika, coriander, cumin, turmeric, cinnamon, allspice, and cayenne to make the shawarma spice blend.
In a medium bowl, toss the dried chickpeas with the olive oil. Spread on the prepared sheet in a single layer. Roast 15 minutes, until starting to firm and turn golden.
Remove pan; sprinkle 2 tbsp of the spice blend over the hot chickpeas and toss on the pan to coat. Roast 8–10 minutes more, until crisp and fragrant.
Meanwhile, make the garden medley: in a medium bowl, combine the cucumber, tomatoes, red bell pepper, red onion, and ½ cup finely chopped fresh mint.
Make the Lemon-Tahini Cream: in a small bowl, whisk the yogurt, tahini, lemon juice, lemon zest, and garlic. Whisk in water, 1 tbsp at a time, until smooth and drizzlable. Season with black pepper.
Warm the pitas until soft. Cut the top off each to form a pocket. Spread a generous layer of hummus inside, add crispy chickpeas, a spoonful of the garden medley, and garnish with a few whole mint leaves. Finish with a generous drizzle of Lemon-Tahini Cream and serve immediately.