For the peach puree: Toss the drained peaches into a food processor or high speed blender. Puree until smooth. Leftover puree will keep well in the fridge for up to a week.
In your favorite glass, combine 2 oz peach puree with the coconut rum. Stir, then fill with ice. Pour over the prosecco, then top with sparkling water. Garnish with peach slices.