To prepare the dough, in a large bowl whisk together the flour, sugar and salt. In a separate bowl whisk together the egg yolk, vanilla and ice water. Slowly pour into the flour mixture, mixing until combined. Cut the butter into the mixture with a pastry blender until pea-size clumps form. Knead the dough into a ball, then pat flat and wrap with plastic wrap. Refrigerate for 30 minutes.
After the dough has chilled, roll it out into a circle approximately ⅛" thick. Place into a tart pan with a removable bottom. Trim the dough so that it is flush with the rim, then place a piece of aluminum foil over top and freeze for 30 minutes. Place in the oven and bake at 375 degrees for 20, remove the foil and continue baking for an additional 5-10 minutes or until golden brown.
To poach the pears, in a large dutch oven or stock pot, combine the apple juice and orange juice and bring to a simmer. Add the pears and boil for 5 minutes, then reduce heat to a low simmer and continue cooking for 10 minutes or until pears are tender. Remove and allow to cool on a plate.
Meanwhile, to make the filling, grind the almonds, flour, cinnamon and cardamom in a food processor. Sprinkle in the sugar, add the butter and extracts. Mix until smooth, add the egg and continue mixing until the egg is incorporated.
Preheat oven to 350 degrees, spread the filling evenly in baked crust. Cut each pear in half lengthwise, remove cores, then cut crosswise into thin slices. Slide a spatula under the "halves" and place on top of the filling with the narrow ends towards the center.
Place in the oven and bake until the filling has set and the top is golden brown, about 40-50 minutes. Remove from the oven and allow to cool for 30 minutes before removing, cutting and serving.