Lightly butter a 10-inch tart pan with a removable base and set it aside. In a food processor, combine flour, sugar, salt, and lemon zest. Pulse until evenly mixed. Add the chilled butter cubes and continue pulsing until the mixture forms a crumbly texture with no visible butter chunks. Add the egg yolk and vanilla extract, then pulse again until the dough starts forming clumps. The mixture might seem dry at first—keep pulsing and it will gradually come together.

Transfer the dough and loose bits onto a clean work surface. Using the heel of your hand, knead until it transforms into a cohesive dough that resembles sugar cookie dough. Press the dough into the greased tart pan, ensuring it’s pressed evenly and firmly into the base and sides. Aim for a thickness just under ¼ inch. Chill the tart shell in the refrigerator for at least 1 hour or freeze for a minimum of 30 minutes.

For preparing in advance, form the dough into a disc, wrap in plastic, and refrigerate up to 2 days. Before rolling, allow the dough to sit at room temperature for 15–20 minutes. Roll it out between sheets of parchment or wax paper and gently transfer it to the tart pan. Patch any cracks with your fingers and press the dough into all the edges for a uniform shell. This dough is forgiving and can also be frozen for up to a month.

While the dough is chilling, begin poaching the pears. In a 3-quart saucepan, stir together cold water and sugar. Heat over medium, stirring occasionally, until the sugar dissolves completely. Stir in cinnamon sticks, star anise, lemon peel, and vanilla.

Peel the pears carefully, keeping the stems intact. Rub each peeled pear with the lemon half to prevent browning. Core the pears from the bottom using a paring knife or melon baller. Gently lower the pears into the simmering poaching liquid, ensuring they’re almost entirely submerged.

Bring the mixture to a low simmer. Cover the surface with a round of parchment paper and let the pears cook for 12 to 15 minutes, turning occasionally to ensure even poaching. The pears should be tender but not soft or mushy. Use a knife to test for doneness by piercing the base—there should be minimal resistance.

Allow the pears to cool in the poaching liquid until they reach room temperature. You may store them in the poaching syrup in the fridge for up to a week. The aromatic syrup can also be repurposed as a base for cocktails or used again for poaching.

Preheat your oven to 375°F (190°C) with a rack in the middle. Line the chilled tart shell with greased foil, shiny side down. Fill with pie weights, dried beans, or sugar. Bake for 20 minutes, then carefully remove the foil and weights. Return to the oven and bake for another 10 to 15 minutes, or until the crust turns lightly golden and is fully set. Transfer to a wire rack and let it cool completely before filling.

In the bowl of a stand mixer fitted with a paddle attachment, or using a hand mixer, cream together the softened butter and sugar until smooth and fluffy. On low speed, gradually add the almond flour and eggs, alternating between the two, until blended. Add the flour, then mix in vanilla, lemon zest, and optional dark rum until just incorporated. If not using immediately, store in the refrigerator.

Set the tart pan on a baking sheet. Spread the frangipane evenly into the cooled shell using an offset spatula. Place the poached pears on paper towels to absorb excess syrup. Halve the pears lengthwise, remove the stems and remaining core, then slice crosswise into thin, even slices.

Using a wide spatula, gently lift each fanned-out pear half and place it on the frangipane with the narrow end pointing toward the center. Repeat with remaining pears, spacing them evenly in a circular arrangement.

Bake at 375°F (190°C) for 40 to 55 minutes, or until the frangipane puffs up around the pears and turns a deep golden brown. If your oven tends to run hot, lower the temperature by 25°F. If the edges brown too quickly, shield them with a loose ring of foil. Ensure the center is fully baked before removing.

Cool the tart in the pan on a rack until it reaches room temperature or is just slightly warm. Carefully remove the tart ring before serving.

Before presenting, dust lightly with powdered sugar. This tart is best enjoyed the same day it’s baked. Serve as-is or with a dollop of freshly whipped cream. Store leftovers at room temperature for up to 2 days.