Place mint leaves in the bottom of a glass cup or traditional silver cup. Add the sugar and muddle the mint and sugar together, breaking down and bruising the mint and making sure the sugar is dissolved. Fill glass with finely chopped ice. Pour bourbon over the ice. Stir well; add more ice if needed. Garnish with a few sprigs of mint.
Note: If you like your mint julep a touch sweeter, make a mint simple syrup and add 1-2 teaspoons, depending on taste.