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Place 1 of the circles on a parchment paper lined baking sheet. Pipe a 5-inch diameter mound of almond cream in the center of the circle. The mound should be about 1-inch high. Prepare the egg wash: Whisk together the egg yolks, whole egg, and milk in a small bowl until well combined.
Lightly brush the remaining 1 1/2-inch rim of the pastry circle with the egg wash. Place the second circle of puff pastry over the first. Gently press against the sides of the almond cream mound to remove any trapped air. Seal the edges of the 2 layers by pressing the top edge into the bottom edge. Use a sharp knife to give the circle a fluted edge like a flower. Use a sharp knife to pierce a 1/2-inch slit in the top layer at the center. This will allow steam to escape during baking. To make the classic pattern in the top, use a sharp knife to score a curved line that begins at the top of the mound and ends at the bottom of the mound. Repeat this line every 1/2 inch around the circumference of the mound, but be careful not to cut through the top layer and into the almond cream. Lightly brush the top with egg wash.
Let the frangipane rest in the refrigerator for 1 hour before baking. (At this point, you can wrap the frangipane well in plastic wrap and freeze for up to 2 weeks. Let it thaw in the refrigerator or in your backpack before baking.) Preheat the oven to 350 degrees F (175 degrees C). Bake until it begins to brown slightly, about 20 minutes. Meanwhile, prepare the glaze: Stir together the corn syrup and water.
Remove the frangipane from the oven and brush it well with the corn syrup mixture. This adds sweetness, enhances the color, and gives it a crispy crust. Continue to bake until well risen and evenly browned, about another 20 minutes. The baked frangipane should be flaky and tender, and the almond cream center still moist. Remove the baking sheet from the oven and let cool on a wire rack. The frangipane is best when served while it is still slightly warm. Use a serrated knife to slice it.