Make basil sugar for the glass rim by combining 1/4 cup sugar and leaves from 1 basil sprig in a food processor. Pulse until the basil leaves are fully incorporated, and you can no longer see whole pieces of leaf in the sugar.

Pour basil sugar onto a plate. Wet the edges of a small glass with water, and roll the cup onto the basil sugar to form the sugar rim. Fill glass with ice.

In a cup or drink shaker, combine blackberries, simple syrup, sliced basil leaves, and juice from 1/2 lime. Macerate with a cocktail muddle or a wooden spoon. Add about a cup to a cup and a half of ice (depending on the size of your cup or cocktail shaker). Add tequila, and shake vigorously for 10-15 seconds.

Pour through a strainer into the prepared glass. Serve with lime wedges and fresh blackberries.