Pit and slice the peaches. Peel the ginger, and loosely chop into smaller chunks. Use a juicer or your hands to squeeze the lime juice into a bowl. If using your hands, make sure to strain out any seeds.
Next, set aside a couple pieces of basil, and add all the rest of the ingredients into a blender and until it forms a purée. Pour into fun glassware, garnish with the basil leaves that you had set aside, serve, and enjoy!