For the simple syrup: Combine the sugar and 2 cups water in a small saucepan and cook over low heat, stirring, until the sugar dissolves. Let cool. The syrup will keep in a sealed container in the refrigerator for up to 1 month.
For the lime fizz: Add the egg to the cup of a dry cocktail shaker. In order, add 30 grams (about 1 ounce) simple syrup, the lime juice, gin and then rum. Shake until frothy. Add ice and shake again. Pour into a highball glass. Top with club soda and garnish with the lime wheel. Put a spoon and straw into the glass before serving.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.
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