Whisk prosecco, water and sugar in a saucepan just wide enough to hold the pears. Place the pan over medium heat and continue whisking until sugar is dissolved. Add the lemon zest, lemon juice and the pears.
Bring to a boil, then reduce heat to a simmer. Cook until pears give no resistance when pierced with a paring knife, 30-40 minutes, gently turn the pears in the syrup a few times as they cook.
Cool the pears in the syrup to room temperature. The pears can be covered and chilled in the refrigerator up to 3 days before serving.
Beat ricotta in a bowl with the sugar until lightened and smooth. Scrape the vanilla bean seeds into the ricotta and stir.
Serve the pears in shallow bowls with a little of the syrup spooned over them. Put a generous spoonful ricotta alongside each pear. Break the biscotti or shortbread into large pieces and place on the side of the bowl.
I used small, firm Bartlett pears. You can use another variety of green pear or russet-colored Bosc, just be sure they're not too ripe and soft or they'll get mushy when cooked.
Cooking time could vary depending on the size of the pears, but count on at least 30 minutes.