Pour 45 ml absinthe and 10 ml simple syrup into a rocks glass.
Fill the glass to the rim with crushed ice.
Swizzle or churn with a bar spoon for 15-20 seconds, until the outside of the glass frosts over.
Top with 30 ml soda water and add more crushed ice to form a dome.
Garnish with a mint sprig and serve with a short straw.
The frost is the whole point — swizzle hard enough that the glass ices over, since the melting crushed ice is what dilutes the absinthe to drinkable strength.
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