Set a wire rack on top of a rimmed baking sheet. Pat the chicken dry on all sides with a paper towel, then set on top of the rack.
In a small bowl, whisk together 1 Tbsp kosher salt, ½ tsp black pepper, 2 tsp sugar, 2 tsp lemon zest, 2 Tbsp chopped tarragon, 1 grated clove of garlic, and 1 tsp paprika. Rub the brine all over the chicken, being sure to coat it evenly on all sides. Cut the lemon in half, then reserve for roasting.
Season inside the cavity with a little kosher salt, then add a handful of fresh tarragon sprigs and a halved lemon. If you like, use kitchen twine to truss the chicken. Roast until the internal temperature on the thickest part of the chicken registers 165F.
Meanwhile, set the cast-iron skillet over medium-high heat. When hot, add dry white wine and 1 Tbsp sherry vinegar, then use a spatula to scrape any browned bits off the bottom. Cook until the sauce has reduced by about half. Do not let the sauce boil once the cream has been added.
Serve immediately with sauce spooned on top or on the side. Sprinkle the chicken with flaky sea salt. Enjoy!