For the Thyme Simple Syrup:In a medium saucepan, combine the sugar and thyme with 2 cups water. Heat over medium heat, stirring occasionally, until the sugar has dissolved, about 2 minutes. Remove from the heat and let the thyme infuse for 20 minutes. Strain the syrup and let it cool. Discard the thyme leaves. Set aside 3 tablespoons of the syrup and reserve the rest in the refrigerator for up to 2 weeks.To Assemble: Combine the bourbon, lemon juice, and reserved 3 tablespoons simple syrup in a cocktail shaker with ice. Shake well and strain into a cocktail glass over fresh ice (thyme-infused optional). Garnish with a lemon twist and a sprig of thyme. Serve immediately.