Muddle blackberries and simple in a shaker tin, then add all the rest. Shake with ice and pour into old fashioned glass. I garnished with a little twist of lemon and a couple extra blackberries.
That looks very similar to the Bourbon Bloom I got at Perry's Steakhouse. They added mint and St Germaine Elderflower. It was so good that I bought a bottle of the St Germain to make it at home. Recipe video if you'd like to try it yourself https://youtu.be/7kc4S6DrlBw