Cut lime half crosswise into four slices and drop into an Old-Fashioned style cocktail glass.
Sprinkle coarse brown sugar over the lime slices. Muddle gently until juicy.
Fill glass to the brim with ice. Add cachaça until glass is 2/3 full.
Pour glass into metal half of a Boston-style cocktail shaker . Join glass with the shaker and shake briskly for 10-15 seconds.
Separate the glass from the shaker, pour the Caipirinha from the shaker back into the glass, and serve.
Bartender's hint: If you don't own a Boston shaker, or if you don't have a serving glass that fits into the metal half of the shaker, you can improvise and use a conventional cocktail shaker: Prepare the ingredients in your serving glass as described above, transfer to your shaker and shake well, remove the lid from the shaker, and pour the Caipirinha back into the original serving glass. A fair amount of undissolved sugar will have remained in the bottom of the serving glass so give the drink a quick stir before serving.