A very good galette of kings

The cake of kings is a tradition that I follow every year. Scrupulously. Because it's important to follow the traditions... Yes, well, it's above all very good.
Before, a long time ago, I used to buy it ready-made. Until the day when someone told me that it was actually very simple and I had to try. Maybe not puff pastry, but frangipane isn't a witch.
I confirm, it's very simple. Well, I tested several recipes, I missed some of them (the frangipane, too liquid, came out on all sides). My cake wasn't as good as the pastry cakes, but it was good and it was already good.
And then this year, I followed Anne Papilles and Pupilles' recipe, and once again, it changes everything. I threw my old recipe in the fire and then I made another one. I'll give you the recipe, with my little changes.
• 2 puff pastries (I tried several but for me it's Picard who makes the best)
• 80 g sugar
• 2 eggs
• 1 sachet vanilla sugar
• 10 g cornstarch
• 10 cl almond milk (or cow's milk)
• 150 g almond powder
• 50 g butter
• 1 tablespoon of rum (not obligatory but it smells good)
• 1 teaspoon bitter almond extract
• 1 little milk to brown the dough
• 1 to 2 beans.

To get started

• Take the butter out of the fridge so that it is soft when you start making the recipe, as well as the puff pasta if it is frozen (but not 1 hour before either because if it is too defrosted, the paper will not remove properly).
• Beat the 2 eggs and sugar. Dissolve cornstarch in cold milk and add to egg-sugar mixture. Cook the mixture over low heat, stirring constantly with a wooden spoon. The mixture will thicken gradually until boiling. Leave to thicken a little more out of the heat.
• Place the cream obtained in a container. Add the almond powder and chopped soft butter, bitter almond extract and rum.
• Preheat oven to 200°C.
• Place one of the two puff pasta, without removing the baking paper, on the baking sheet. Spread the almond cream - more or less homogeneously - without putting any on the edges so that they can be welded together with the paste from above (1 to 2 cm), and place the beans (rather towards the edges so as not to find them too quickly). Lightly wet the edges with fingertips.
• Take the second dough, always with its baking paper, and cover it with the filling. Remove the paper (this is where the exercise is difficult if the dough is too thawed). Re-assemble the edges of the bottom on top dough to close the wafer. Weld with fingertips (as if the paste were one). To be sure that nothing will come out, I make small streaks with the tip of a knife on the edges.
• To do like the chiefs, draw round circles or arcs from the middle.
• Brown with milk, without touching the edges.
• Bake downstairs for about 40 min under supervision.

Useful hint

The wafer is cooked when it no longer folds when you try to lift it.
Try not to eat it as soon as you get out of the oven, it's better when it's warm.