In a medium skillet, heat olive oil and saute garlic and onions over medium-low heat for 3 minutes. Add tarragon, salt, and pepper, and cook for 1 minute; do not let the mixture brown. Remove from heat and let cool.
In a large bowl, combine the shrimp with the onion mixture and lemon juice, stirring until well coated. Let rest at room temperature for 30 minutes.
Preheat the broiler. Arrange the marinated shrimp in a skillet. Cover the shrimp with any remaining marinade.
Broil under high heat until the shrimp are pink and the topping is well browned, approximately 5 minutes. Serve immediately.