Make black cherry spread by heating cherries with sugar, adding lemon sugar mixed with pectin, bringing to a boil, and roughly blending.
Make the basque dough by rubbing together flour, baking powder, powdered sugar, salt, and cubed cold butter. Add vanilla and egg yolks and mix until well combined.
Roll out more than half the dough into a 5mm thick disk and place in a fluted tart pan.
Make the pastry cream by bringing milk and a quarter of the sugar to a boil with vanilla, then tempering the egg yolk and sugar mixture with the hot milk and cooking for 2 minutes.
Cool the pastry cream, then flavor it with almond extract and almond milk to make a frangipane cream.
Assemble the gâteau basque by coating the bottom of the tart shell with black cherry spread and topping with the almond pastry cream.
Roll out the remaining dough into a thin round disk, freeze for 10 minutes, and use to enclose the cake.
Chill the assembled cake, then brush it twice and score with a fork to create the perfect cross pattern.
