Ingredients
1 envelope (1/4 ounce or 2 1/4 teaspoons) active dry yeast (not rapid-rise)
1 cup warm milk (110°F)
1 vanilla bean, split and seeds scraped
4 1/2 cups plus 2 tablespoons unbleached all-purpose flour (1 1/4 pounds), and more for dusting
1/2 cup sugar
1 tablespoon kosher salt (we use Diamond Crystal)
4 sticks (2 cups) unsalted butter, room temperature, cut into tablespoons
2 large whole eggs plus 1 large yolk, room temperature
1 bottle (750 milliliters) dry white wine, such as Sauvignon Blanc
Grated zest of 1 lemon, plus 2 tablespoons fresh juice
1 cup sugar
2 cinnamon sticks
1 vanilla bean, split and seeds scraped
8 small pears, such as Bartlett (about 2 pounds), stems left on, peeled, halved lengthwise, and cored
4 tablespoons unsalted butter, room temperature
1/4 cup sugar
2 large eggs, room temperature
1/2 cup finely ground blanched almonds
1 tablespoon dark rum, such as Myers's
1/2 teaspoon pure almond extract
2 tablespoons unbleached all-purpose flour
Preparation
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.
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.)
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.)
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.
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.
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.
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.
