Basque Cake with Pastry Cream Filling

There are as many versions of gâteau basque as there are people who bake it, and the Basques like nothing better than to sit around and discuss the relative merits of one baker’s recipe versus another’s. It’s like listening to Toulousains talk about cassoulet, Provençals arguing about bouillabaisse, or Alsatians quarreling over choucroute. A combination cake and pie, gâteau basque is stuffed with pastry cream flavored with almonds, anise, rum, orange-flower water, and Armagnac