Preheat the oven to 375 degrees Fahrenheit and line a baking sheet with parchment paper.
Unwrap the puff pastry sheet and cut it along the seams, yielding three long rectangles. Subsequently, cut each rectangle into three equally sized squares.
Repeat the process with the second pastry sheet.
Arrange these squares on a baking sheet lined with a piece of parchment paper, ensuring they are about an inch away from each other. Create a border by scoring the crust approximately half an inch from the edge of each square.
Beat the egg in a small bowl. Using a pastry brush, coat the outer crust of each tart with the beaten egg.
Spread a spoonful of fig jam within the scored lines, top with the pear slices, add the blue cheese on top of the pear, and finally add a few sprigs of thyme.
Using the middle rack in the oven, bake for 18-22 minutes until the edges turn a dark golden brown and the puff pastry is thoroughly cooked.
Cool on a wire rack or cooling rack before serving. Enjoy!