Dissolve the salt and sugar in 2 cups cold water. Place shrimp in brine, cover and refrigerate for 15 minutes. Remove shrimp from brine, pat dry with paper towels. Remove the shells and set aside.

Heat 1 1/2 teaspoons oil in skillet over high heat until it shimmers. Add shrimp shells and cook, stirring constantly until slightly brown and spotty, 2-4 minutes. Remove skillet from heat and add vermouth and thyme. When bubbling stops, return skillet to medium heat and simmer, stirring occasionally for 4 minutes. Strain through a colander set over a bowl. Discard shells and reserve the liquid. Wipe out skillet with paper towels.

Combine lemon juice and cornstarch in small bowl and set aside. Heat remaining 1 tablespoon oil, garlic and pepper in skillet over medium heat until garlic is fragrant, but not browned. Add reserved vermouth mixture, increase heat to medium, add shrimp, cover and cook, just until shrimp is opaque. Remove skillet from heat and with a slotted spoon remove shrimp to a bowl.

Return skillet to medium heat, add lemon juice and cornstarch mixture and cook until thickened, about one minute. Remove from heat, whisk in butter and parsley until combined. Return shrimp and any accumulated juices to skillet and toss to combine. Serve with buttered egg noodles, steamed basmati rice or toasted crusty bread.