Cut a sheet of thawed frozen puff pastry lengthwise into five strips, then cut crosswise into thirds to make 15 rectangles. Slice each rectangle diagonally to make 30 triangles. Spoon 1/2 teaspoon goat cheese onto each triangle and top with a quartered fig. Wrap the pastry around the fig and press to seal. Place on a parchment-lined baking sheet, brush with beaten egg and bake at 400˚ until puffed and golden, 18 to 20 minutes.