Poached Pear and Frangipane Tart with Bittersweet Chocolate Sauce

Sift the all-purpose flour, powdered sugar, and fine sea salt through a fine mesh sieve into a large mixing bowl.

Add the cold cubed butter to the flour mixture and cut it in using a pastry blender or fingertips until the mixture resembles coarse breadcrumbs with no butter pieces larger than pea-sized.

Add the egg yolk and mix gently with a fork, drizzling up to 15 ml of cold water if dry, until the dough clumps together into a cohesive mass.

Shape the dough into a flat disc approximately 2 cm thick, wrap tightly in plastic wrap, and refrigerate for 60 minutes.

Peel the pears smoothly using a vegetable peeler, slice each pear in half lengthwise on a cutting board, and remove the core, seeds, and fibrous stem using a melon baller and paring knife.

Combine 600 ml water, 150 g granulated sugar, 15 ml lemon juice, and 5 g vanilla bean paste in a medium saucepan, bring to a gentle boil over medium heat to dissolve sugar, submerge the pear halves, reduce heat to low, cover with a parchment circle, and simmer at 85°C (185°F) for 15 minutes until just knife-tender.

Lift the poached pears out of the hot syrup using a slotted spoon, arrange cut-side down on several layers of paper towels over a cutting board, and leave to cool completely and drain excess syrup for 20 minutes.

Dust a clean work surface lightly with flour, place the chilled dough disc down, and roll outward with a rolling pin from the center into a uniform round approximately 28 cm in diameter and 3 mm in thickness.

Gently lift and line the dough into the 9-inch fluted tart pan, pressing it firmly into the fluted corners without stretching, trim excess dough flush with the rim by rolling over the top with the rolling pin, and dock the bottom evenly with a fork.

Transfer the lined tart pan to the refrigerator and chill for 20 minutes to relax the gluten and solidify the butter.

Preheat the oven to 180°C (350°F) with a rack set in the center position.

Line the chilled pastry shell with a sheet of crumpled parchment paper, fill to the rim with pie weights, bake at 180°C (350°F) for 15 minutes, carefully remove the parchment and weights, and bake for an additional 5 minutes until the base looks dry and set.

In a medium mixing bowl, beat 80 g softened butter and 80 g granulated sugar using an electric hand mixer on medium speed for 3 minutes until pale, light, and creamy.

Add the beaten room temperature egg, 10 ml dark rum, and 1 g fine sea salt to the creamed butter, beating on medium-low speed until fully incorporated and emulsified.

Add 80 g almond flour and 10 g all-purpose flour to the bowl, then gently fold with a silicone spatula until a uniform, spreadable paste forms.

Place the drained pear halves on the cutting board and, using a sharp chef's knife, slice each half crosswise into 4 mm thick slices, keeping the shape of each half intact.

Spread the frangipane evenly over the bottom of the par-baked tart shell using a silicone spatula, then gently lift each sliced pear half with the flat of a knife, slide onto the almond cream radiating outward like clock spokes with tapered ends facing inward, and press lightly to fan the slices.

Bake the assembled tart at 175°C (350°F) for 40 minutes until the frangipane puffs up between the pear slices, turns deep golden brown, and registers at least 71°C (160°F) in the center.

Transfer the tart pan to a wire cooling rack and allow the tart to cool undisturbed for 45 minutes before gently pushing the removable bottom up to unmold.

In a small saucepan, combine 120 ml heavy cream and 40 ml whole milk, then heat over medium-low heat until bubbles break along the edge and the mixture reaches 85°C (185°F).

Place the 120 g finely chopped dark chocolate, 15 g butter, and 1 g fine sea salt into a heatproof mixing bowl, pour the hot cream mixture directly over the top, let rest for 60 seconds, and whisk in small concentric circles from the center outward until a glossy, silk-smooth sauce forms.

Transfer the unmolded tart to a cutting board and slice into 8 equal wedges using a sharp chef's knife, wiping the blade clean between cuts, then arrange individual slices on dessert plates.

Ladle approximately 30 ml of warm bittersweet chocolate sauce alongside or generously across each tart slice and serve immediately.