Make the thyme syrup: Add sugar, water, and thyme to a small saucepan. Bring to a gentle simmer, stir until sugar dissolves, then turn off heat. Let it steep 10 minutes, strain, and cool.
Muddle the berries: In a cocktail shaker, add blackberries.
Gently muddle until juicy but not pulverized to seeds.
Add the base: Pour in vodka, lemon juice, and thyme syrup. Fill the shaker with ice.
Shake hard: Shake 10–12 seconds until the shaker is frosty. This chills and slightly dilutes for a smoother sip.
Strain: Double strain into a chilled coupe for a smooth finish, or strain over fresh ice in a rocks glass for a more relaxed serve.
Optional fizz: Add a small splash of soda water or dry tonic if you want it lighter and spritzy.
Garnish: Add a thyme sprig, a few blackberries, and a lemon wheel.
Serve right away.