Combine pear nectar, cinnamon sticks, nutmeg, cloves, and Allspice in a medium saucepan. Bring to a boil over medium heat. Remove from the heat, cover, and let stand at least 1 hour. Remove the cinnamon sticks and discard.
Transfer the pear mixture to a pitcher and refrigerate for at least 3 hours.
For each drink, fill champagne flute 1/3 of the way with pear juice. Top with Prosecco.