Preheat grill to medium (350°F to 400°F). Stir together butter, garlic, lemon zest and juice, thyme, pepper, and 1 teaspoon of the salt in a medium bowl until well combined.
Toss together shrimp, oil, and remaining 1 teaspoon salt in a large bowl. Grill shrimp, covered, just until shrimp are bright red and charred, 2 to 3 minutes on each side. Toss with lemony garlic butter, and serve immediately.
Fisher's at Orange Beach Marina, Orange Beach, AL