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Prepare the grill (high heat). Using a knife, cut the back of the shrimp. Brush the shrimp with oil. Sprinkle with salt. Grill the shrimp until just cooked through, about 3 minutes per side. Transfer the shrimp to a plate.
Toss the pasta with the pesto in the large bowl to coat, adding the reserved cooking liquid 1 tablespoon at a time to moisten. Top with the grilled shrimp. Garnish with the lemon zest and parsley.