Sift together flour, sugar, and salt in a large mixing bowl. Cut in butter using a pastry cutter or your fingers. Stir together egg yolk and vanilla in a small bowl, then work into flour mixture until it resembles coarse cornmeal. Add 3 tbsp. ice water, 1 tbsp. at a time, mix until dough holds together, then form into a ball, cover with plastic wrap, and refrigerate for 1 hour.
Preheat oven to 400°. Roll out dough into a 14'' round on a lightly floured surface; ease into a 12'' tart pan with removable bottom and prick all over with a fork. Cover with aluminum foil, fill with pie weights or dried beans, and bake for 20 minutes. Carefully remove foil and weights and set shell aside to cool. Do not turn off oven.
For filling, bring 4 cups water and 1 1⁄2 cups sugar to a boil in a large saucepan over medium-high heat. Reduce heat to low, halve pears, and poach until tender, 20–25 minutes. Remove, allow to cool, then cut out cores.
Combine 1⁄3 cup almonds and confectioners' sugar in a food processor. Grind just until fine. Scrape seeds from vanilla bean into milk and bring to a boil in a small saucepan over medium heat. Combine eggs, remaining sugar, and flour in a large saucepan, slowly whisk in hot milk, and cook, whisking, over medium heat until thick, 3–6 minutes. Transfer to a mixing bowl, add almond meal and butter, and stir until butter melts. Set aside to cool.
Spoon cooled custard into tart shell. Lay pears, stem end inward, in custard and bake until crust is golden brown, about 30 minutes. Preheat broiler. Sprinkle amaretti and remaining almonds on top, dust with confectioners' sugar, and broil until brown, about 2 minutes. Serve warm, with crème anglaise if desired.