1Set blood orange on a cutting board and, using a sharp knife, cut off and discard ends. Slice rind and white pith off fruit using a gentle downward sawing motion, cutting away as little flesh as possible. Discard rind.
2Slice fruit into 1/2-inch pieces. Divide pieces evenly among the wineglasses.
3Sprinkle 1/2 teaspoon sugar atop orange slices in each glass and muddle together to extract juice. Add 1/2 teaspoon vermouth to each glass and stir.
4Divide sparkling wine among the glasses, stir, and serve.