Place shrimp in a large mixing bowl. Add lemon juice, olive oil, chopped green onion, minced garlic, ground saffron, salt, pepper, and thyme; stir well. Cover and refrigerate 1 hour, stirring mixture occasionally.
Drain shrimp, reserving marinade. Combine marinade and butter in a medium saucepan. Cook over medium heat, stirring occasionally, until butter melts. Set mixture aside, and keep warm.
Place shrimp on a broiling pan. Broil 4 inches from heating element 3 minutes; turn and broil an additional 3 minutes or until done.
Remove shrimp to a warm serving platter, and sprinkle with chopped fresh parsley. Serve warm with prepared sauce of your choice.