In a small saucepan, combine all ingredients for the simple syrup. Bring to a boil over medium-high heat. Once sugar has dissolved, remove from heat. Cover and steep for 15 minutes. Strain and let syrup cool in a medium bowl to room temperature, about 15 minutes.
Add all ingredients into a shaker filled halfway with ice. Shake well until chilled thoroughly, about 20 seconds.
Strain into two double old-fashioned glasses filled with ice.
Garnish each with a lemon wheel, thyme sprig and blackberries.