Mix the cider, pomegranate juice, and apple brandy in a glass measuring cup or pitcher until combined. Chill until ready to serve.
To make a Bubbletini, pour about 1/4 cup of the cider mixture into a chilled martini glass. Top with ice-cold Prosecco. To garnish, either very thinly slice the apple crosswise on a mandoline slicer and float the wheel in the cocktail, or cut thin wedges from the apple and garnish the rim.