Sprinkle work surface with 1 tablespoon grated Parmesan.. Unfold thawed puff pastry sheet on Parmesan. Lightly beat egg with 1 tablespoon of water. Lightly brush puff pastry with egg wash.
In a medium bowl, combine 2 tablespoons Parmesan, Italian cheese blend, and paprika. Sprinkle over surface of pastry sheet. Lightly press cheese into pastry.
Fold top and bottom edges of pastry to the center. Next, fold pastry in half from left to right. Now, fold in half top to bottom. Wrap and freeze at least 30 minutes.
Preheat oven to 400 degrees F. Line baking sheet with parchment paper; set aside.
Cut 1/8-inch thick slices starting a the shortest edge. Sprinkle "faces" of palmier with remaining parmesan cheese and lay "face" up on prepared baking sheet, two inches apart.
Bake in preheated oven for 20 minutes. Serve warm or at room temperature.