Prepare the tarragon sauce by whisking together the sour cream, tarragon, mustard, and lemon juice in a small bowl. Season with salt and pepper to taste, then cover and set aside in the refrigerator until ready to serve.
Heat a heavy frying pan over high heat until it’s very hot. Brush the shrimp lightly with oil on both sides, then add them to the pan in a single layer. Cook for 2 minutes, turning once, until the shrimp turn pink and start to curl.
Keeping the heat on high, pour in ⅔ cup of the wine along with the garlic. Let the mixture boil rapidly for 2–3 minutes to reduce slightly and concentrate the flavors. Stir in 2 tablespoons of the chopped parsley.
Once the wine has reduced a bit, lower the heat to medium and add the remaining wine to the pan. Season with salt and pepper, then let everything simmer gently for 5 minutes. During this time, the shrimp will release their natural juices into the wine, creating a flavorful broth.
Spoon the aromatic cooking juices over the shrimp to glaze them beautifully. Sprinkle with the remaining parsley and garnish the dish with lemon wedges and fresh tarragon sprigs for an elegant presentation. Serve immediately while hot, with the chilled tarragon sauce on the side for dipping.