Add the blackberries, mint leaves, and sugar to a food processor or blender. Cover and puree until smooth and combined. Allow to sit for a couple of minutes.
Using a fine mesh sieve over a bowl and a spatula, press the puree through to remove the seeds and fruit pulp.
Pour ½ ounce of the blackberry mint puree into the bottom of each champagne flute.
Slowly and carefully, fill each glass with champagne or Prosseco. (Pour carefully so it doesn't bubble over and make a mess!)
Garnish with a sprig of mint, if desired, and serve. Or hide away in your bedroom closet and drink them all yourself. Whatever you prefer!