Saute apples gently in hot butter, until browned. Let stand in skillet for 1/2 hour with the brandy, cinnamon and first 1/3 cup sugar.
Blend together the milk, additional 1/3 cup sugar, eggs, vanilla, salt and flour for a full minute until well blended and frothy. It is best in a blender, but a hand mixer will work as well.
Butter a fireproof baking dish. Pour a 1/4 inch layer of the batter in the dish and set over moderate heat for a minute or two until a film of batter has set in the bottom of the dish. Remove from heat.
Spread the apple mixture over the batter layer. Pour on the remaining batter and smooth the surface with the back of a spoon.
Place in the middle of an oven preheated to 350 and bake for about an hour. The clafoutis is done when it has puffed and browned and a needle or knife plunged in to its center comes out clean.
Sprinkle the top with powdered sugar just before serving. It is best served warm or hot. It will sink slightly in the center.