This delicious, golden, flaky pastry cake encases an almond cream filling (frangipane). Hidden somewhere within is a china figurine (une fève). Traditionally, the person who finds the fève in their slice of cake is the king or queen for the day, and entitled to wear the paper crown that comes with the cake. Pastry chef Ken Larsen of Brasserie in New York City created this recipe.
Cream together the butter, sugar, and almond paste. Scrape down the bowl. Add the eggs one at a time, followed by the flour, and mix until incorporated. Fill a large pastry bag with the cream and create a 1-inch diameter opening by cutting off the tip. Set aside.
Preheat the oven to 350 degrees.
Roll out each sheet of puff pastry to an 8 ½-inch circle. Each circle should be about 1/8-inch-thick. Line a baking sheet with parchment paper and transfer 1 of the circles to the sheet. Starting from the center of the circle, pipe a 5-inch diameter and 1-inch-high mound of almond cream, leaving a border of approximately 1 ½ inches.
Whisk together the egg yolks, egg, and milk in a small bowl until well combined. Brush lightly on the border. Place the second circle of puff pastry over the first, pressing gently against the circumference of the almond paste mound, in order to remove any trapped air.
Seal the edges of the 2 layers by pressing the top edge into the bottom edge. (This will keep the almond cream from running out as it bakes.) Use a sharp paring knife to make diagonal indentations all around the sealed edges, creating a flower effect.
Next, pierce a ½-inch slit in the center in order to allow the steam to escape while baking. (You can make a pattern on top if you wish.) Prepare the glaze by stirring together the corn syrup and water in a bowl.
Place the galette in the oven for about 20 minutes, until it begins to brown. Remove from the oven and reduce the temperature to 330 degrees. Brush the galette with the glaze. (This adds sweetness, enhances the color, and gives it a crispy crust.)
Place the galette back in the oven for an additional 15 minutes, until the crust has risen and is browned evenly. Remove from the oven and cool on a wire rack. The galette is best when served still warm. It should be flaky and tender, and the almond cream center should be moist. Slice with a serrated knife.