Butter the bottom of a heavy bottomed pan with 4 Tbs. of the butter. Sprinkle with half of the sugar. Peel the apples, core and slice thickly. Pack into the bottom of the skillet. Sprinkle on the rest of the sugar and dot with 2 Tbs. of butter. Cover and cook over high heat for 5 minutes. Remove cover and cook over moderate heat for 15 minutes or so, until the sugar has caramelized and is pale brown. Meanwhile, to make the pastry, place the flour and salt in a bowl. Cut in the remaining 10 Tbs. butter with two knives or a pastry cutter. When the mixture resembles breadcrumbs, make a well in the center and pour in a mixture of the water and egg yolk. Bring the mixture into a ball with the fingers of one hand and then knead briefly. Chill the dough wrapped in plastic. When the apples are ready, roll out the dough and place it over the apples. Tuck in the edges all around. Bake the upside-down tart in a preheated 350 degree oven for about 30 minutes. When the pastry is cooked, remove the tart from the oven and turn over onto a serving plate. Some of the apples may stick to the pan. Just scrape them off and rearrange them on the tart. If the tart is not dark enough, sprinkle with additional sugar and run under the broiler. Decorate with the sliced almonds and serve with the flavored whipped cream. Serves 6-8.