In a small saucepan, simmer water, sugar, and fresh ginger for 10 minutes. Strain into a glass jar and cool.
For the Peach Mojito
Cut half of the lime into circles and the other half into wedges. Cut half the peach into half-round slices and the other half into small chunks.
In a tall glass, add 3-4 lime wedges, 6-8 fresh mint leaves, the peach chunks, 2 ounces simple syrup and muddle until juices are released from lime and peach.
Fill two glasses with ice, add a lime round or two and a couple peach slices to each glass. Top each with 2 ounces of rum, half of muddled fruit mixture, and a splash of sparkling water (or to taste). Garnish with peach, lime and fresh mint sprig. Cheers and Enjoy!