Instructions

1. Make the crust: In a medium bowl, whisk together the flour, sugar, and salt. Using a pastry blender, two forks, or your fingers, incorporate the butter into the flour mixture until pea-size crumbs form. Drizzle in 3 tablespoons of ice water, then use a fork to gently combine until the dough comes together and still has visible pieces of butter. (Alternatively, in a food processor, pulse together the flour, sugar and salt. Add the butter in batches, pulsing until pea-sized crumbs form, followed by 3 tablespoons of ice water.) Shape into a ½-inch-thick disk, wrap in plastic, and refrigerate for at least 1 hour. 
2. Remove the dough from the refrigerator and set aside until soft enough to roll, about 15 minutes. On a lightly floured surface, using a floured rolling pin, roll the dough into a 13-inch circle. Transfer to a 9-inch fluted tart pan with a removable base, gently pressing the dough into the corners of the pan (do not stretch it). Using a sharp knife or scissors, trim the edges all the way around to a 1-inch overhang. Transfer the pan to a large, rimmed baking sheet and refrigerate until firm, about 15 minutes.
3. Position a rack in the center of the oven and preheat to 425°F. Line the chilled pie shell with parchment paper or greased aluminum foil and fill it with pie weights or dried beans. Bake until the edges are golden brown, about 25 minutes, then remove from the oven. Carefully lift out the parchment and pie weights and transfer the pan to a wire rack to cool. (If the bottom isn’t baked through, turn the oven to 350°F and bake for another 5–10 minutes.)
4. Meanwhile, make the poached pears: To a medium pot, add the honey, hibiscus, cardamom, pears, cinnamon sticks, and star anise and add enough water to cover by 1½ inches. Bring to a boil, then turn the heat to medium-low and cook until the pears are just tender, 15–20 minutes. Remove from the heat and set aside to cool and infuse, about 30 minutes.
5. Using a slotted spoon, transfer the pears to a plate. (Reserve the leftover liquid for another use; see headnote.) Thinly slice the pears lengthwise, keeping the halves together so that they fan more evenly, and set aside.
6. Make the frangipane: In a stand mixer fitted with the paddle attachment, beat the butter, sugar, and lemon zest together at medium speed until light and fluffy, about 4 minutes. Beat in the vanilla and eggs, then add the almond flour and all-purpose flour and mix until homogeneous and pale, using a silicone spatula to scrape down the sides halfway through, about 1 minute. Scrape the filling into the cooled crust and, starting in the center of the pan, overlap the pears in concentric circles in one even layer. Bake until the filling is golden brown, puffed, and fully set, about 30 minutes. Cool to room temperature before unmolding and serving.