Melt the butter in the microwave and let it cool for a few moments.
In the bowl of the stand mixer, place the cold water, then the melted butter, salt and finish by adding the flour.
Mix at medium speed with the hook for about 2-3 minutes, just until the dough is smooth.
Take the dough out of the bowl and form a ball with your hands.
Cut the dough in the center crosswise with a knife (see picture).
Wrap the dough with cling film and place it in the fridge for at least 2 hours.
Cut a sheet of baking paper, place the butter in the center and close the baking paper over the butter to form a square. (see picture)
Using a rolling pin, spread the butter to obtain a 6 inch square baking sheet about 1.5 cm thick.
Place the butter sheet in the fridge.
Take out of the fridge the dough and the butter plate (they should have about the same temperature).
First roll out the dough to form a square slightly larger than the butter plate, place the butter in the center of the dough and fold the corners of the dough over the butter to cover it completely. (see picture)
Roll out the dough with a rolling pin to obtain a long rectangle.
Proceed to the first folding by making a double turn (see picture), then turn the dough a quarter turn (so that the opening is always on the right) and immediately proceed to a single turn (see picture).
Wrap the dough in cling film and leave it to chill in the fridge for about 1h30 - 2 hours.
Make a double turn again, turn the dough a quarter of a turn and make a single turn again, let the dough chill in the fridge for another 2 hours.
Take the dough out of the fridge and this time make only 1 single turn and let the dough rest for another 1 hour in the fridge.
In a bowl, beat the butter with the powdered sugar.
Add the eggs one by one and mix well between each addition.then finish by adding the almond powder.place in the frigde.
Place the milk and scraped half vanilla bean in a saucepan over medium heat, bring to a boil and let stand for 15 minutes.
In a bowl, whisk the egg yolks with the sugar until white, then add the flour.
Remove the vanilla bean and pour the milk into the bowl containing the yolks, flour and sugar, then whisk and return to the pan.
Bring this mixture to the boil for 2 minutes, beating all the time.
Pour the custard into a container, cover with cling film on contact and place in the fridge until cool.
Mix the almond cream and the custard cream with an electric whisk for 1 - 2 minutes.
Assembly & decoration of the galette des rois
Roll out the puff pastry to a thickness of 3 mm, using a 10 inch tart ring or a large plate, cut out 2 circles of puff pastry.
Place the first circle on a baking tray with a baking sheet.
Place a layer of frangipane using a pastry bag, leaving a sufficient gap between the cream and the edge.
Using a pastry brush, apply a thin layer of water to the edges.
Cover with the second layer of pastry.use a thin knife to scratch the top of the cake.
Brush on a layer of egg yolk.
Place your galette in the fridge for 30 minutes or 10 minutes in the freezer.
Baking the Galette des rois
Brush on a second layer of egg yolk and bake at 356°F / 180°C for about 45-50 minutes.