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Simmer the water and sugar together over medium heat until the sugar has completely dissolved. Take off the heat and add the basil leaves. Cool completely and strain through a fine mesh strainer, pressing on the leaves.
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In a food processor blend together the peach and blackberries until smooth. Strain through a fine mesh strainer, pressing on the pulp to extract all the juice.
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Mix together the salt and gochugaru. Run a wedge of lime along the rim of two glasses, dip in the salt mixture, coating evenly.
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Fill each glass with ice, add an ounce of tequila to each glass, a tablespoon of thai basil simple syrup, top with juice and squeeze a lime wedge into each glass. Stir until well mixed.