Preparation

Make the sweet pastry dough:

• Put the butter, confectioners’ sugar, salt, and vanilla in a food processor; process until very soft, smooth, and well blended. Sift together the two flours. Add them and pulse just until incorporated; the dough will look slightly crumbly. Add the egg and process agian until smooth and creamy.
• Scrape the dough onto a lightly floured work surface. Divide it and shape each half into a disk. Wrap each disk well in plastic wrap and chill for at least an hour. (You’ll only use one disk for this tart; freeze the other one for up to four months.)
  

Roll the dough and then line the tart pan

• Let the dough rest at room temperature for 10 to 15 minutes so it softens slightly. Unwrap it and place it on a lightly floured work surface. Roll the dough into a round, using even pressure and turning the disk a quarter turn after each pass of the rolling pin. Flour the work surface and the dough very lightly as needed. Continue rolling until the dough is a shade more than 1/8 inch thick and very even.
  

• With a docker or a sharp-tined fork, prick the entire surface of the dough. Gently roll the dough around the rolling pin and transfer it to a 9-inch tart pan. With the pricked side of the dough facing down now, unroll the dough round and drape it over the pan, taking care not to stretch it.
  

• With your thumb, carefully push the dough down into the pan where the base and sides of the pan meet, and then push the dough carefully onto the sides of the pan, pinching to make neat, straight upper walls.
  

• With a paring knife, trim off any overhang so the dough doesn’t extend higher than the pan. Chill the lined tart pan for at least 1 hour.

Make the frangipane

• Heat the oven to 325°F. Cream the butter with an electric mixer until it’s light and fluffy, about 5 minutes. Add the sugar and continue to cream well. Add the ground almonds, flour, and yolks, blending well after each addition. The mixture should be light and fluffy.
• Put the frangipane in a pastry bag with a wide tip and pipe an even layer into the chilled tart shell.
  

• Bake in the heated oven until the shell is thoroughly browned on the sides and the bottom and the frangipane is a deep gold, 40 to 50 minutes. Cool the tart, still in the pan, on a rack.

Make the pastry cream:

• In a saucepan, heat the milk with the vanilla pod and seeds until it steams; let it steep, off the heat, for a few minutes. In a small bowl, whisk the egg yolks, sugar, and flour. Pour a bit of the hot milk into the yolks and whisk to blend.
• Pour the yolk mixture into the rest of the milk and put the pan back on medium heat, whisking constantly and rapidly until the mixture boils; let it boil for 1 minute, still whisking, and then take it off the heat. Pour the pastry cream into a bowl; put a piece of plastic wrap directly on the surface of the cream and chill at least 1 hour. Beat the chilled pastry cream with a mixer or a wooden spoon until it’s lighter, looser, and lump-free.
  

• Whip the cream until it holds soft but definite peaks. Carefully fold the whipped cream into the pastry cream.
  

Put it all together:

• Put the cream into a pastry bag with a wide tip and pipe an even layer into the shell.
• Arrange the fruit in a pretty pattern, placing the pieces upright when possible. With a clean pastry brush, coat the fruit with a thin layer of the apple jelly to glaze.