Toast pistachios on a small sheet pan at 325°F (165°C) for 6–8 minutes, shaking once, until fragrant and slightly deeper in color. Transfer to a cool plate immediately.
Place dried broccoli florets and stem matchsticks in a wide mixing bowl. Add chickpeas, radishes, red onion, dates, and parsley.
Whisk yogurt and tahini together until smooth, then whisk in lemon juice, olive oil, honey, garlic, cumin, salt, and pepper. Add cold water 1 tablespoon at a time only if the dressing does not fall in a thick ribbon from the whisk.
Pour about three-quarters of the dressing over the broccoli mixture and fold gently from the bottom until everything is lightly coated. Add more dressing only where dry pockets remain.
Cover and refrigerate for 30 minutes, until the broccoli tastes seasoned at the cut edges but still snaps cleanly.
Fold in half the toasted pistachios just before serving, then scatter the remainder over the surface.