The national drink of Brazil uses cachaça, the rumlike liquor made from sugarcane. It is a muddled drink, like a mint julep, only with lime and sugar instead of mint and sugar. Bruising the lime quarters and sugar with a pestle or the back of a spoon releases flavorful oils and juice from the rind of the fruit and gives the cocktail its fresh, bright flavor.
Combine the lime quarters and sugar in a cocktail shaker. Muddle until juices have released and sugar is mostly dissolved. Add the crushed ice and cachaça; cover and shake vigorously until thoroughly chilled. Pour contents of shaker into a chilled rocks glass. Garnish, if desired.