To make the thyme simple syrup, add thyme, water, and sugar for the syrup in a small saucepan. Place over high heat and bring to a boil, stirring until the sugar is dissolved.

Remove syrup from heat, cover and let steep for 15 minutes. Remove thyme sprigs and cool to room temperature before making the cocktail.

Add blackberries and lime juice for the cocktail to a mixing glass. Muddle together.

Add gin and syrup, then fill with ice. Stir to combine.

Strain into two cocktail glasses filled with ice, dividing the cocktail evenly between the glasses.

Top each glass with tonic water. Garnish with fresh blackberries and thyme. Serve.