1. flour 7 tablespoons butter, salt and 2 teaspoons of sugar in a food processor, beat until fluffy crumb (10-12 seconds). Pour cold water and whisk still 6-8 times. Put the dough on a cutting board and molded him the ball, and then the disc. If the dough is too sticky, add a couple tablespoons of flour. Wrap in plastic wrap and refrigerate for at least an hour.
2. When the dough is ready, start to warm up the oven to 190 degrees.
3. Roll out the dough and transfer to a round baking pan. Make a small rim of dough. Make a few holes in the dough with a fork and close the base foil (shiny side of the foil grease with butter, which should come into contact with the test). Foil tightly need to flatten the dough to make it completely encircle it.
4. Bake the base for 15 minutes. Cool before stuffing.
5. For the stuffing chop 2, 5 apples into thin slices. Melt the remaining 3 tablespoons of butter in a frying pan, cast the seeds from the vanilla pod and pod itself, add the brown sugar and chopped apples. Cook over high heat, stirring occasionally, until apples zakaramelizuyutsya (about 2 minutes).
6. Pour rum and cook until apples are tender (around 6 minutes). Throw pieces of sliced bananas, remove and discard the vanilla pod. Pour this filling into the chilled base.
7. Cut the remaining 1, 5 apples thinly. Put the stuffing on top, sprinkle with a tablespoon of sugar and bake for 45-50 minutes until the tart apples are soft and do not podzolotyatsya.
8. Remove the cake from the oven and brush with melted apricot jam (for shine). Cool completely before serving.