Recipe courtesy of François Payard. For more information about chef Payard, his bakeries, or his King's Cake, visit his website.
Mix the almonds and sugar in the bowl of an electric mixer. Then, add the creamed butter, two whole eggs, almond extract, and the rum, mixing until well combined.
Divide the puff pastry dough in half and roll out each half into a 12-inch circle. Lay one pastry round on a very slightly greased baking pan. Pour the filling in the middle of the disc and spread it around without allowing it to reach the edge. Drop the toy into the filling.
Carefully top the filing with the second circle of dough. Press firmly around the edge with moist fingers to seal the “cake.” Brush the surface of the pastry with the remaining egg yolk. (For a little more control over the color, brush the yolk on roughly halfway through the baking).
With a knife or a fork lightly draw curved lines into the top of the “cake” for decoration. Then, make a few tiny cuts on the top to let out steam during cooking.
Cook the pastry for about 35 to 40 minutes in preheated 400-degree oven. Oven temperatures can vary so be sure to remove the cake once it’s golden. Cool and then serve while still warm, if possible.