Chill a martini glass in the freezer for about 10 minutes or fill it with ice water while you prepare the drink.
Add the blackberries to a cocktail shaker and gently muddle until they release their juice and resemble a thick puree.
Pour in the vodka, triple sec, fresh lemon juice, and simple syrup. Stir briefly to combine the ingredients.
Fill the shaker with ice cubes, seal it tightly, and shake vigorously for 15–20 seconds until the outside feels very cold.
Empty the chilled martini glass and double strain the cocktail through a fine mesh strainer into the glass to remove seeds and pulp.
Garnish with a fresh blackberry and a sprig of rosemary or basil if desired. Serve immediately while well chilled.