Mound the flour on the work surface, mix with salt and sugar, Make a well in the center of the flour. Cut the cold butter into small pieces. Add the butter and egg to the well. Use a pastry cutter or 2 table knives to work the dough until it resembles a coarse meal. Gather the dough into a ball . Wrap in plastic and refrigerate about 30 minutes.
Rinse the apples, peel, remove cores and stems, and cut into quarters.
Brush the tart pan with 50 grams (1 3/4 ounces) butter. Scatter a thick layer of sugar (approximately 100 grams/3 1/2 ounces) over the butter and arrange the apple quarters in concentric rings over the sugar.
Heat the cake pan over direct medium heat for about 10 minutes. Remove from heat when the sugar begins to caramelize. Allow to cool briefly, then sprinkle the apples with remaining sugar. Cut the rest of the butter into small pieces and dot the surface evenly with the butter pieces.
Roll out the dough, place it over the filling, and tuck the edges down into the mold.
Bake the tart in an oven preheated to 220°C (approximately 425°F) for 30 minutes. Let the tart cool in the pan for a few minutes, then unmold onto a platter. Serve warm.