Heat the oven to 190 C. Place the flour in a food processor with butter and sugar and mix until it forms a fine, breadcrumb-like mass. Add the egg yolk and 1-2 tablespoons of cold water and work to form a firm dough.
Prepare the mold for the cake. Briefly roll the dough on a lightly floured surface and then roll out to a full circle about 5 cm larger than your mold. Place the dough on the erased baking sheet with a roller and then push it into the corners with your finger. Do not cut the dough. Put baking paper on top of the dough for a while and pour the beans on it and let it rest for 10 minutes. Then take off the bean paper and put the dough in the oven for 5 minutes.
To prepare the filling, place the sugar in a large pan with 3 tablespoons of cold water. Heat gently with stirring to dissolve the sugar. When the sugar is completely dissolved, raise the temperature and bubble until the syrup has a rich caramel color. Remove from the heat and stir in the butter until dissolved, then stir in the cream. Return to the fire and cook, stirring constantly, until the sauce is thick enough to leave a gap at the bottom of the pan after cutting with a spoon. Finally, stir in the walnuts.
Pour the nut mixture onto the dough and level it with a fork. Put in the oven for 8-10 minutes until the filling bubbles. Finally, let the cake cool and serve.