Instructions

MAKE THE PATE BRISEE: In a large bowl, blend flour, butter, shortening and salt until it resembles coarse meal. Add ice water and toss until water is incorporated. Form dough into ball. Knead dough lightly with heel of hand against smooth surface to distribute fat evenly, then reform into ball. Dust with flour and chill in waxed paper at least 1 hour.
On a floured surface, roll out the Pate Brisee to 1/8 inch thick in the approximate shape of your serving tray. Drape it over the rolling pin and unroll it onto a baking sheet. Trim dough to the shape of the serving tray but slightly smaller. Chill
MAKE THE PUFF PASTRY: In a large bowl, sift together flour and salt. Add cold butter and blend until it resembles coarse meal. Add ice water and incorporate into dough. Work dough to combine and form into a ball. Dust lightly with flour. Cut a deep cross in the middle of ball and push each quarter outward to form a 4 inch square. Pat until smooth and chill in waxed paper.
Knead 3/4 c. butter, squeezing through fingers. Form into rough square, then put in between sheets of waxed paper and roll into a 4 inch square. Remove paper and dust on all sides with flour. Wrap in waxed paper and chill until firm but not hard.
Roll dough into 7 inch square on floured surface. Lay square of chilled butter diagonally in center of dough and roll 4 visible corners of dough into 4 inch lengths. Fold each strip of dough over the butter to enclose, then turn the whole thing over. Sprinkle board and dough with flour and roll to 10x6 rectangle. Arrange dough so that a short side is toward you. Brush off excess flour, fold top 1/3 down over the center and fold the bottem third over the top. Turn so that open side faces you. Uniformly roll dough from the center away from you. Do not roll pin over the ends. Reverse the strip on the surface, flouring as necessary, and again roll dough away from you to make the rectangle 10 inches long again. Brush off excess flour and fold in thirds as before. Chill 30 minutes. Make two more turns, folding as before, always starting with the open end near you. Chill for 30 minutes, or up to a week. Give the dough 2 more turns before using.
Roll half of puff pastry into 3/16 inch thick rectangle, reserving the remainder for another use. Cut the rectangle into enough 3/4 inch strips to fit around the edge of Pate Brisee. Moisten the edge of the Pate Brisee and arrange the strips on moistened areas and trim to fit. Prick bottom of shell with fork and chill for 20 minutes. Line shell with waxed paper and fill with pie weights. Make an egg wash of 1 egg and 1 T. cream well beaten. Brush puff pastry with the wash and bake in the lower third of a 400 degree oven for 15 minutes. Remove weights and paper and continue baking for 10-15 minutes or until golden. Release shell from baking sheet, slide onto wire rack and let cool.
MAKE THE CARAMEL SAUCE: In a skillet, combine sugar and butter and bring to a boil over low heat, stirring and washing down sugar crystals with brush dipped in cold water, until sugar is dissolved. Increase heat to medium-high and cook, rotating pan gently, until golden caramel in color. Remove from heat and stir in cream.
Spread shell with caramel, let caramel cool completely and transfer shell to serving tray. Cut enough 1/2 slices of banana to cover the pastry bottom.
MAKE THE RUM SYRUP: In a saucepan, combine all the ingredients and bring to a boil over medium-low heat, stirring and washing down the sugar crystals with a brush dipped in water. Simmer syrup for 5 minutes. Poach bananas in batches of rum syrup for 3 minutes and with slotted spatula, transfer half of the slices to pastry shell, arranging them in one layer. Reserve the remainder for later.
MAKE THE ALMOND PASTRY CREAM: In the bowl of an electric mixer, combine egg yolks, small egg and sugar. Beat at medium speed until light and lemon colored. Gradually add flour and beat until smooth. Remove bowl from mixer and add milk in a steady stream while whisking. Transfer to a heavy saucepan and bring to a boil over medium-low heat, stirring, for 2 minutes. Remove from heat and beat in butter until melted and combined. Stir in the rum, almonds and vanilla. Let cool, covered with buttered waxed paper on surface of cream. Fold in whipped cream.
Fill the shell with the Almond Pastry Cream, spreading it evenly. Arrange the rest of the banana slices on top.
MAKE THE APRICOT GLAZE: In a saucepan, combine jam and rum. Bring to a boil over medium heat, stirring frequently. Strain through a fine sieve. Brush the top of the tart with the glaze.