Add the blackberries and simple syrup to a cocktail shaker. Muddle until the blackberries are well-pulverized.
Add the tequila, orange liqueur, fresh lime juice and a handful of ice to a cocktail shaker. Put on the top and shake vigorously until well-chilled, about 15-30 seconds.
If you'd like a salted glass, run a lime slice along the rim of the glass to moisten. Sprinkle coarse sea salt on a small plate and swirl the rim into the salt.
Replace the cocktail shaker top with a cocktail strainer and strain into an ice-filled glass. Garnish with additional lime slices and blackberries if desired. Enjoy!
