Preheat oven to 400 degrees Fahrenheit.
Finely chop the rosemary. Using a mortar and pestle, mash the rosemary to release its aromatic oil. Drizzle in the olive oil and stir to mix. Set to the side to allow the rosemary to infuse the oil. We’ll use this for brushing our puff pastry.
Sprinkle your all-purpose flour over a sheet of parchment paper and layout your thawed puff pastry. Using a knife, slice the puff pastry into 2-inch by 2-inch squares. Place the sliced puff pastry squares on the prepared baking sheet. Using that same knife, make small slits along the sides to create a small border on each square, about ¼ inch border all around. Do not cut all the way through. We want to create a border for arranging our fig slices so their juices don’t run over the pastry during the bake.
Brush the pastry squares with the rosemary infused olive oil.
Remove the stems and slice figs into ¼ inch slices, lengthwise. Arrange the slices on each of the puff pastry square, taking care to not overlap them over the border. You will place anywhere from one to two slices depending on how big the figs are.
Crumble the blue cheese and nestle it amongst the fig slices. Brush any last bits of the rosemary oil over the top.
Bake for 25 to 30 minutes until the edges are golden brown, crispy, and the filling is slightly bubbling.
Remove from oven and cool for 5 minutes before serving. Garnish with chopped fresh rosemary and a drizzle or the fig syrup.