Slice a thin layer off the bottom of each pear to make a flat surface. Stand the pears cut-side down in a 9-by-13-inch baking dish. Whisk together the honey and 1 cup water and pour over the pears. Add the star anise and cinnamon sticks. Cover with foil and roast until the pears are tender and the liquid has reduced, about 45 minutes. Let cool.
Place the pears in the bottom of a large pitcher and add the red wine and elderflower liqueur. Refrigerate overnight.
When ready to serve, pour the pear sangria into large glasses over Cranberry Ice Cubes and garnish with mint. Top each drink with a splash of cava.
Cranberry Ice Cubes:
Put 2 to 3 cranberries in each compartment of an ice cube tray and fill with water. Freeze until set.