Dissolve the 3 tablespoons salt and 2 tablespoons sugar in 1 quart of cold water in a large gallon-size freezer ziplock bag. Add the 1 ½ pounds of shrimp to the brine and refrigerate for 15 minutes (no longer or the shrimp will turn mushy). Remove shrimp from brine and pat dry with paper towels.
Heat 1 tablespoon oil in a 12-inch skillet over high heat until shimmering. Add the shrimp shells and cook, stirring frequently, until they begin to turn spotty brown, 2 to 4 minutes. Remove skillet from heat and carefully add the 1 ½ cup of wine and the 5 thyme sprigs. When bubbling subsides, turn the heat to medium and return the skillet to stove. Simmer gently, stirring occasionally, for 5 minutes. Strain mixture through a sieve over a large bowl. Discard shells and reserve the liquid (you should have about 2/3 cup). Wipe out skillet with paper towels.
Combine 3 tablespoons lemon juice and 1 teaspoon cornstarch in a small bowl. Set aside. Heat remaining 1 tablespoon oil, sliced garlic, red pepper flakes, and black pepper in the now-empty skillet over medium-low heat, stirring occasionally, until the garlic is fragrant and just beginning to turn golden at edges, 3 to 4 minutes. Add the reserved wine mixture, increase heat to high, and bring to a simmer. Reduce heat to medium now, add the shrimp, cover, and cook, stirring occasionally, until the shrimp are just opaque, not yet fully cooked, 5 to 7 minutes. Remove skillet from heat and using a slotted spoon, transfer shrimp to a bowl.
Return the skillet to medium heat, add the lemon juice-cornstarch mixture, and cook until slightly thickened, this should happen very quickly. Remove from heat and whisk in the 4 tablespoons of butter and 1 tablespoon of chopped parsley until butter has melted. Return shrimp and any accumulated juices to the skillet and toss to combine. The shrimp should be fully cooked but not over-cooked now, between resting in the bowl and being added back to the sauce mixture.
You can serve the Shrimp Scampi a couple of ways at this point. Serve it in the pan it cooked in and eat the shrimp family style, using forks and passing lemon wedges to squeeze over the Scampi. If serving as an appetizer, this is a good way to display the Shrimp Scampi, too. Either in the pan or on a plate as I've illustrated.If serving over pasta, be frugal with the amount of pasta used, as the Scampi is not super saucy.See notes for storing and reheating leftovers.