Prepare your puff pastry. Thaw a sheet of frozen puff pastry according to the package instructions. Let sit at room temperature until pliable, then cut into six rectangles.
Cut each pear in half, then slice thinly from the middle section outward. Use a Mandoline slicer if you have one, and try to get each slice as thin as you can.
Transfer pears to a bowl, and pour Cheerwine syrup over the slices. Use your hands to mix the slices into the syrup and make sure they are each well coated.
Line a baking sheet with parchment paper, and lay out your puff pastry rectangles. Using each piece as a guide, remove the piece, and then add a teaspoon of honey in its place directly on the parchment paper. Lay 2-3 paper-thin slices of pear on top of the honey, and then replace the puff pastry rectangle on top. Press the pastry down using your fingers to create a seal over the fruit. Repeat with each of the remaining pieces of pastry.
Bake for 15-20 minutes or until pastry edges are golden brown and crisp. Remove from the oven, and let the tray rest for five minutes before flipping tarts over with a wide, flat metal spatula.