On a lightly floured surface or a sheet of parchment, roll your thawed puff pastry into a 12’’ square.
Using a small offset spatula, spread about 2 ½ Tbsp of the fig jam into a thin layer to the edges of the pastry. Top with ⅔ c of the Parmesan cheese and pat into the jam. Fold the top and bottom edges towards the center, creating a smaller rectangle.
Spread another layer of fig jam, about 1 Tbsp, and 1/3 c Parmesan cheese. Press the cheese into the jam and fold the edges towards the center once more. Apply the remaining jam and ¼ c of cheese, then fold the two sides on top of one another to create a heart-shaped log. Gently press together, wrap in plastic, and refrigerate for 15-20 minutes.
Using a sharp knife or kitchen string, cut the log into 16 slices, about ¾’’-1’’ thick. Place on a lined baking sheet a few inches apart, brush with egg wash, and sprinkle with remaining ¼ c of Parmesan cheese.
Bake for 15-25 minutes, rotating halfway through baking. Remove from the oven when the palmiers are golden brown. Serve warm.