Leave the puff pastry to thaw at room temperature for 20-30 minutes.
Preheat oven to to 400˚F. Line a baking sheet with a parchment paper. If the caramel is thick or cold, scoop 3 tablespoons into a small microwave bowl. Microwave for 5 seconds and set aside.
For the pears, washed, pat dried and peeled. Cut in half and remove the core and seeds using a metal spoon. Cut into ⅛-inch slices. Add to a medium bowl. Add lemon juice, turbinao sugar, and cinnamon. Toss gently to combine. Set aside for at least 15 minutes.
On a lightly floured working surface, unfold the puff pastry and roll into 9 x 12-inch rectangle with a rolling pin. Cut into 9 (4 x 3-inch) rectangles. Transfer to the prepared baking sheet, spacing them apart from each other.
Using a sharp knife, score a border around the entire edge (do not cut through), about ¼-inch thick. Then prick all over the center rectangle with a fork. Brush a thin layer of caramel sauce in the center rectangle. Transfer the whole baking sheet to the fridge for 15 minutes.
After 15 minutes, place about 4 slices of pears on top of each rectangle. They can be overlap. Make sure they fit within the border. Brush the top with more caramel. Then brush the edges lightly with heavy cream and sprinkle with sugar.
Bake in the oven for 18 - 20 minutes, until the pastry is golden brown on top and bottom. Remove from oven and transfer to a cooling rack. Cool slightly before serving.
To serve, scoop ½ tablespoon caramel sauce into a small microwave bowl. Microwave for 5 seconds. Drizzle over the tarts. Best serve warm or at room temperature.