For the poached pears: In a medium saucepan, bring 4 cups (1 L) water to a boil with the sugar, cinnamon stick, cloves, and star anise. Lower the heat to a low simmer while you prepare the pears. Peel the pears, remove the stems, cut them in half, and core them. Add the pears to the saucepan, bring back to a boil, then lower the heat again. Simmer the pears for 10 to 15 minutes, or until you can easily pierce one with a sharp knife. Drain (keep the syrup to add to smoothies, oatmeal, or cocktails) and set the pears aside to cool. If preparing in advance, store the poached pears in an airtight container and refrigerate for up to 1 day.
For the crust: In a mixing bowl, combine the powdered sugar, almond flour, all-purpose flour, and salt. Add in the butter and egg, and mix with a fork or your hands to form a smooth ball. Wrap with plastic wrap and refrigerate for up to 1 day.
For the pastry cream: In a small bowl, whisk together the egg yolks, sugar, and cornstarch. In a medium saucepan, combine the milk, cream, and vanilla, then bring to a simmer. While whisking, slowly pour the egg mixture into the saucepan. Whisk continuously for 2 to 3 minutes, or until the mixture thickens to a glistening cream. Remove from the heat and let cool to room temperature.
For the frangipane: In a mixing bowl, beat together the butter, powdered sugar, almond flour, and eggs. Incorporate the rum and almond extract.
Pour the cooled pastry cream over the frangipane and mix to thoroughly combine. If preparing in advance, transfer to an airtight container and refrigerate for up to 1 day.
To assemble and bake the poached pear and almond tart: If you made them in advance, take the components of the tart out of the refrigerator 30 minutes before baking. Set a rack in the middle of the oven, then preheat to 350°F (175°C). Lightly grease an 11-in (28-cm) tart pan with a removable bottom(see note) and set aside.
Place the crust between two large sheets of parchment paper, then roll it out to a 12-in (31-cm) circle. Peel the top sheet of parchment paper off the pastry, then flip the crust over to the prepared tart pan. Peel the second sheet of parchment paper off the pastry, then gently ease and press the pastry down into the pan. Poke the bottom of the crust all over with a fork.
Spread the frangipane filling in an even layer into the crust. Top with the poached pear halves, with the outside of the pear facing up (see note.)
Bake for about 45 minutes, or until the crust is golden brown and the filling is puffed and golden. Transfer the tart to a cooling rack and cool for at least 2 hours before serving.
SERVING: Right before serving, lightly dust with powdered sugar and sprinkle with sliced almonds.
STORAGE: Keep leftover tart under a cake dome at room temperature for a couple of days, or in the refrigerator, uncovered, for up to three days. Refrigerating the tart uncovered will ensure the pastry remains crisp. Always bring the tart back to room temperature before serving it again.
Audrey advises to make this tart in a 9-in (23-cm) pan, but I found I had enough crust and filling to make an 11-inch (28-cm) pan. You could try using a deep-dish pie dish, but in any case, make sure not to overfill the pan because the filling puffs up significantly upon baking.
You can place pear halves straight over the frangipane, or for a different look, slice them thinly almost all the way up to the tip of each pear half, then gently press to fan them out. Set over the frangipane filling and bake as indicated.