Preheat oven to 350 degrees. Cut 4 pieces of parchment paper to measure 12 square inches each. Juice lemon into a small bowl. Halve each pear horizontally. Dip cut sides of pear in lemon juice (to prevent browning). Using a melon baller, remove core from each half.
Place 1 star anise in cored center of each pear. Drizzle 1 tablespoon honey over each star anise.
Place a pear half, cut side up, on each piece of paper. Working with one piece at a time, hold pear half in paper in the palm of your hand; gather edges of paper around fruit with your free hand. Transfer to a rimmed baking sheet.
Pour 1 tablespoon vermouth into pear half in parchment. Twist paper tightly around top of each fruit to seal. Bake 45 minutes; pears should be tender. Transfer packets to shallow bowls. Serve immediately, opening packets at the table.