Heat olive oil in a large skillet and sauce garlic and onions with salt and pepper over medium-low heat for 3 minutes. Add tarragon and cook for 1 minute. Do not let the mixture brown. Remove from heat and let cool.
Combine shrimp with onion mixture and lemon juice in a large bowl, stirring well. Cover and let stand 30 minutes.
Preheat broiler to high. Arrange shrimp in a large oven-proof skillet. Pour any remaining marinade over shrimp. Broil 5 minutes or until shrimp are pink and topping is browned. Serve immediately.