In a cocktail shaker combine 4 blackberries and 2 sprigs rosemary. To muddle, gently crush berries and rosemary with the back of a spoon. Add tequila, lime juice, and Simple Syrup. Add ice cubes; cover and shake until very cold. Strain liquid into an ice-filled glass. If desired, garnish with additional blackberries and a rosemary sprig.
In a small saucepan combine sugar and water. Bring to boiling over medium heat, stirring until sugar is dissolved. (The syrup is done when it is completely clear and the surface is covered with bubbles.) Remove from heat; cool. Store, covered, in the refrigerator up to 2 weeks.