Add blackberries and simple syrup to a shaker; muddle well to release juices.
Add lime juice and vodka, then fill the shaker with ice. Shake gently for 5–10 seconds.
Fine-strain into a chilled copper mug or glass filled with fresh ice.
Pour in ginger beer, then top with champagne or sparkling wine. Stir gently to combine without losing bubbles.
Garnish with a lime wedge or mint sprig and serve immediately.
Notes
Skip the simple syrup if using a sweeter sparkling wine; keep it for dry brut styles. For extra fruit, muddle a few raspberries with the blackberries. Use larger ice cubes to slow dilution and keep the fizz lively.