Place plum slices and 2 thyme sprigs in a cocktail shaker and muddle gently to release the flavors without completely crushing the fruit.
Add the vodka or gin, lemon juice, and simple syrup to the shaker.
Fill the shaker with ice and shake vigorously for about 15 seconds until well-chilled.
Double-strain the mixture into a chilled champagne flute or coupe glass to remove any fruit pulp or thyme leaves.
Top with prosecco or champagne, stirring gently with a bar spoon to combine.
Garnish with a fresh thyme sprig and a thin slice of plum on the rim of the glass.
The cocktail should have a beautiful pink-purple hue from the plums.
Serve immediately while the drink is cold and the bubbles are fresh.