In a food processor or a blender process the peaches with blackberries until smooth. Strain through a fine sieve and set aside. This recipe uses 1 oz, reserve the rest for a later use.
For the blackberry peach daiquiri
Add the mint leaves to a cocktail shaker and muddle until bruised and fragrant.
To the same shaker add 1 oz strained blackberry peach puree, rum, simple syrup, lime juice and 6-7 ice cubes. Shake until it's too cold to hold.
Strain into two martini glasses. Garnish with a blackberry.