Preheat oven to 375 degrees. Place the pie dough into a 9" round tart pan. With a fork, dock the shell. (poking holes on the bottom and sides) Place parchment paper over the shell and place dried beans on top to weight down the parchment paper. This will keep the dough from bubbling up when baking. Blind bake the shell for 15 minutes. Remove the beans and parchment paper and cook for another 10 minutes. Remove from oven and cool.
Peel, core, and half the pears. Immediately place the pears in a saucepan with lemon juice and enough ice water to cover them. Add the sugar and the vanilla bean. Cover the pears with a round of baking paper and simmer over medium heat until they are just tender. Remove pears from the syrup and drain to prevent over cooking.
For the Frangipane: Cream the butter with the sugar. Add almond flour and mix until smooth. Add the eggs one at a time and mix until each is absorbed. Stir in the all purpose flour and the rum. Use immediately, or can be stored covered in refrigerator up to four days.
Slice pears 3/8" thick. Fill the cooled tart shell with 12 ounces frangipane about 1/2" thick. Place the pears over the frangipane in a fan pattern. Bake until the shell is lightly golden and the frangipane has risen and colored. About 40 minutes.
Cool and finish with warmed apricot glaze.
For the Apricot Glaze: In a small saucepan, add 3/4 cup Apricot preserves and the 1 tablespoon golden rum. Cook over medium heat until nice and syrupy.
You may make a caramel sauce to accompany the Pear Tart Bordaloue by reducing the liquid in which the pears were cooked to a caramel. Then add heavy cream.