Heat the grill to 190 °C. Roll out the dough into a thin sheet suitable for a pizza baking tray. Peel the pears, remove the cores, cut into thin slices and sprinkle with lime.
Mix the sugar with cardamom. Pile the pears on top of the prepared dough, add the cherries and almond slices, sprinkle the cake with sugar and drizzle with a little butter. Brush the edges of the dough with beaten egg.
Place the cake in the oven on a heated tray, bake the cake until the edges of the dough are nicely colored and the dough is baked, about 20 minutes. Then cut the cake into portions and serve with a spoonful of crème fraîche or sour cream.