Preheat oven to 400 degrees. Line a large baking sheet with parchment paper, set aside.
In a small food processor or blender, place the yogurt, garlic, lime zest, lime juice, cilantro, onion, 1/4 teaspoon salt and crushed red pepper flakes; process to fully combined, set aside.
In a small bowl, mix together the chili powder, cumin, paprika, cayenne pepper, and remaining 1/4 teaspoon salt; set aside.
Unfold the puff pastry and place onto floured work surface. Cut in half width-wise so that you have two rectangles approximately 4 1/2” x 9” each. Set one rectangle aside for another use. Place the other rectangle onto work surface with a long end closest to you. Cutting from a short end, cut 1/4” strips, making 36 strips that measure 1/4” x 4 1/2” each.
Place the shrimp onto a large plate and sprinkle with reserved spice mixture, tossing to coat. Starting at the tail, wrap 1 puff pastry strip around a shrimp, allowing the shrimp to show through, pinching the pastry to itself to seal ends. Place onto prepared baking sheet. Continue to wrap shrimp in this manner until all shrimp are wrapped. Sprinkle shrimp with the dried parsley.
Place in preheated oven and bake until shrimp are cooked through and pastry is lightly browned, approximately 10 minutes.