Melt the butter in an oven-safe skillet (approximately 9-10 inches in diameter) over medium heat. Once melted, sprinkle the sugar evenly over the butter. Cook, without stirring, until the sugar melts and turns into a deep amber caramel. This usually takes about 8-10 minutes. Watch carefully to prevent burning!
Remove the skillet from the heat. Add the lemon juice and swirl the pan to combine. Arrange the pear quarters tightly in a circular pattern over the caramel. You can be creative with the arrangement, but make sure the skillet is filled completely.
Return the skillet to medium heat and cook for 15-20 minutes, or until the pears are slightly softened and have released some of their juices. The caramel will bubble up around the pears.
While the pears are cooking, lightly flour a clean surface. Unfold the thawed puff pastry sheet and gently roll it out to a slightly larger circle than your skillet.
Remove the skillet from the heat. Carefully place the puff pastry over the pears, tucking the edges down inside the skillet to create a seal.
Bake in a preheated oven at 375°F (190°C) for 25-30 minutes, or until the puff pastry is golden brown and puffed up.
Remove the tart from the oven and let it cool in the skillet for about 10 minutes. Place a serving plate over the skillet and carefully invert the tart onto the plate. Be careful, as the caramel will be hot! If any pears stick to the skillet, gently remove them and arrange them on the tart.
Let the Caramelized Pear Tart Tatin cool slightly before serving. Cut into wedges and enjoy!