If your pastry puff sheets are frozen, thaw according to the package directions.
Preheat oven to 400℉.
Add the cinnamon to the granulated sugar and set aside for later.
Cover your baking sheets with parchment paper or silpat mats. For 8 tarts, I use two baking sheets with about 1" in between each tart.
Cut each pastry sheet into 4 equal sized squares and place them on the lined baking pans.
With the sharp point of a knife, score a square frame about ¾" from the edge of each tart pastry. Do not cut all the way through. This will be your frame for the fruit.
Slice the pears in fourths, core them and then thinly slice them (about ⅛" slices).
Work on one baking sheet at a time, keeping the other baking sheet of dough in the fridge to keep the pastry cold. Lay the pears onto the pastry puff square in any order, any design that you prefer. I place them with no regard to the scored frame and then go back and trim them (with my very sharp paring knife) so that they would be within the squared frame.
Melt the butter. Add the vanilla to the melted butter and combine.
Brush the tarts with the butter/vanilla mixture. Brush both the pastry and the fruit.
Liberally sprinkle the sugar/cinnamon on top of each tart.
Bake in the oven for 17 - 20 minutes. Watch carefully at about 15 minutes and take them out once they are a deep golden brown. (In my oven at about 10 minutes, I needed to flip the pans around so that the back tarts cooked the rest of the time in the front of the oven. This made them more evenly golden brown.)
The tarts can be served warm or at room temperature.