Bring 1/2 cup water and 1/2 cup sugar to a boil with fresh thyme sprigs, stirring until the sugar is dissolved. Once boiling, remove from heat and cover, steeping for 30 minutes. Strain and cool completely before using in the cocktail.

Rub the lemon wedge along the rim of a cocktail glass and rim with sugar.

Combine cognac, triple sec, lemon juice and thyme simple syrup in a shaker filled with ice. Shake well and pour into the sugar-rimmed cocktail glass.