How to Make It
Thinly slice 1 cup of the grapes and refrigerate. In a food processor, coarsely chop the remaining grapes in batches. Transfer the chopped grapes to a saucepan and bring to a simmer. Cook until the grapes have released most of their juice, 5 minutes.
Working in batches, strain the grape juice into a bowl, pressing hard on the solids. You should have about 3 1/2 cups of juice; refrigerate until cold.
Divide the sliced grapes equally among 8 Champagne flutes. Pour the chilled fresh grape juice into the flutes and top with the sparkling wine. Garnish each drink with a mint sprig and serve right away.