In a cocktail shaker or sturdy glass, muddle the peach slices with lime juice and honey until the peaches are broken down and juicy.
Add a handful of fresh mint leaves and gently muddle once or twice just to release the oils without tearing the leaves.
Fill two tall glasses with ice and divide the muddled peach mixture between them, straining out large chunks if desired.
Top each glass with 4 ounces of ginger beer and 2 ounces of sparkling water, stir gently, and garnish with fresh peach slices and mint sprigs.