Pour the lime juice into the glass.
Add the sugar and stir until it dissolves in the lime juice. (If using freshly chopped limes instead of lime juice, crush them with the sugar using a pestle until the sugar dissolves.)
Throw in the whole mint leaves, letting them fall where they may, even letting them stick to the sides of the glass. The glass should be loosely full of mint.
Pour crushed ice over the mint leaves to fill the glass.
Using a spoon, stir the ice with the mint and lime until the mint starts to break. Do not break the mint until this point.
Top with 50ml of rum and stir until evenly mixed and the ice is slightly slushy.
Serve with a sprig of mint on top.