Make the mint syrup: Remove the leaves from the mint and reserve for a garnish. Roughly cut the mint stems and place them in a medium saucepan. Add 1 cup water and 2 cups sugar; bring to a simmer for a few minutes until thickened. Remove from the heat and cool for about 1 hour while the mint seeps. When cool, strain into an airtight container. Store in the refrigerator for up to 6 months.
Slice the peaches. Place the berries and peaches on a plate; drizzle with mint syrup and garnish with mint leaves.