Pear-and-Frangipane Pastries

1. Dough: In a small bowl, sprinkle yeast over milk; stir until dissolved. Let stand until foamy, about 5 minutes. Stir in vanilla seeds. In a mixer fitted with the dough-hook attachment, beat together 4 1/2 cups flour, sugar, salt, and 4 tablespoons butter on low speed until mixture resembles coarse meal, 3 to 4 minutes. Add yeast mixture; beat until dough just comes together. Add eggs and yolk; beat until just combined, 2 to 3 minutes (do not overmix). Turn out dough onto a lightly floured surface. Gently knead to form a smooth ball, about 30 seconds. Wrap tightly in plastic and refrigerate at least 2 hours and up to overnight.

2. Switch mixer to the paddle attachment and beat together remaining 3 sticks and 4 tablespoons butter and 2 tablespoons flour. Shape mixture into a 10-by-12-inch rectangle on a sheet of plastic wrap. Wrap and refrigerate at least 15 minutes and up to 1 day. (Before proceeding, let butter mixture stand at room temperature until it has same consistency as dough.)

3. On a lightly floured surface, roll out dough to a 10-by-18-inch rectangle, about 1/4 inch thick, keeping corners square. (Remove any excess flour from dough with a dry pastry brush.) With a short side facing you, place butter mixture over bottom two-thirds of dough. Fold unbuttered third down over butter, then bottom third up over that (as you would fold a business letter; this seals in the butter). Roll out dough again to a 10-by-18-inch rectangle, then fold into thirds as described above; wrap and refrigerate 1 hour. (This completes the first of three turns.) Repeat rolling and folding process two more times, refrigerating at least 1 hour between turns. Wrap tightly in plastic; refrigerate at least 4 hours and up to overnight. (Dough can also be frozen, tightly wrapped in plastic, up to 2 weeks; thaw in refrigerator overnight before using.)

4. Pears: In a large saucepan, bring wine, lemon zest and juice, sugar, cinnamon, vanilla seeds, and 2 cups water to a boil. Reduce to a simmer; add pears and cover with a parchment round to keep submerged. Cook, occasionally turning pears by gently rotating stems with your fingertips, until tender when pierced with a paring knife, about 20 minutes. With a slotted spoon, transfer pears to a heatproof bowl. Return poaching liquid to a boil and continue cooking until syrupy and reduced by half, 10 to 12 minutes. Pour syrup over pears and refrigerate, covered, at least 4 hours and preferably overnight.

5. Frangipane: In mixer fitted with the paddle attachment or a mini food processor, beat together butter and sugar until light and fluffy, about 3 minutes. Add 1 egg, almonds, rum, almond extract, and flour; beat until smooth.

6. Using a slotted spoon, remove pears from poaching liquid and pat dry with paper towels. On a lightly floured surface, roll out dough to a 12-by-20-inch rectangle, about 1/4 inch thick. Using a 3 1/2-inch round cutter, cut out 16 rounds and divide between 2 parchment-lined baking sheets. Fill each pear half with about 2 teaspoons frangipane and place, cut-side down, in centers of rounds. Cover with plastic wrap and let stand in a warm place until doubled in bulk, about 45 minutes.

7. Preheat oven to 375°F. In a small bowl, lightly beat remaining egg. Brush rounds of dough with egg wash, avoiding pears. Bake, rotating halfway through, until pastries are evenly browned, 20 to 25 minutes. Transfer to a wire rack and let cool completely. Serve at room temperature.

Cook's Notes

You can make and freeze the laminated pastry dough up to two weeks ahead of time. Poach the pears the day before assembling the tarts (or at least four hours prior, so they can soak up the lemon-zest, cinnamon, and vanilla flavors in the syrup). When you're ready to bake, thaw the dough, make rounds with a cookie cutter, mix and spread on the frangipane cream, and nestle in the main events.