For the Rhubarb Shrub:
Heat the water in a pot until it steams. Add the sugar and stir until dissolved. Submerge the rhubarb chunks in the sugar syrup over medium heat, being careful not let it boil over. Lower the heat and simmer until all the rhubarb has broken down, stirring occasionally (about 30 to 45 minutes). Remove it from the heat and shock the rhubarb in ice bath with the apple cider vinegar. Strain with progressively finer sieves. Finish through an oil or coffee filter.
To Assemble and Serve:
Combine all ingredients in a soda siphon, chill and charge. Pour over ice in a Collins glass and garnish with basil leaf.