Place apple slices in a bowl. Sprinkle with sugar and 1/4 cup Calvados and allow to macerate 15 minutes. Make batter by placing sifted flour and salt into a warm bowl. Make a well in the center of the flour. Add the yeast, beer, apple juice and olive oil. Combine to form a smooth batter. Cover the bowl and allow the mixture to stand 4 hours. After this period add a little more beer if necessary and fold in the half egg white stiffly beaten. Heat oil for deep frying. Place macerated apple slices into a small frying basket and then place this basket into the batter. Allow all the apple slices to become well coated in the batter. Drain and then place into the hot oil. Fry the beignets for 3 minutes, or until batter is crisp and golden, drain and dredge in confectioner's sugar and serve accompanied by the apricot sauce. Apricot Sauce: Place apricots into a pan on high heat. Add the butter and allow to melt. Flavor with cinnamon. Pour in Slivovitz and light. When flames have almost died down, add the remaining 2 tablespoons Calvados. Add the grated rind of half an orange, and then stir in the cream. Puree in blender and then pour mixture back into the pan and heat. Whisk in the egg yolk and then place sauce into sauceboat. Serve.