Pulse the flour, sugar, salt, and lemon zest in a food processor. Add the cold butter and pulse until no butter pieces show. Add the yolk and vanilla, and keep pulsing until the dough clumps together, even if it looks dry at first.
Knead the dough on the counter until it is smooth, like a soft cookie dough. Press it into the greased tart pan, about a quarter inch thick. Chill it for at least an hour, or freeze it for 30 minutes.
Warm the water and sugar until the sugar dissolves, then add the cinnamon, star anise, vanilla, and lemon peel. Peel the pears, rub them with lemon, core them from the bottom, and lower them in. Cover the pot with a parchment round and simmer for 12 to 15 minutes, until tender but not mushy.
Let the pears cool to room temperature right in the syrup. They keep cooking a little as they cool, so do not overdo the simmer. You can also chill them in the liquid for later.
Heat the oven to 375°F (190°C). Line the chilled dough with buttered foil, fill it with weights, and bake for 20 minutes. Remove the foil and weights, then bake 10 to 15 minutes more, until the shell is lightly golden.
Beat the butter and sugar until creamy. Add the almond flour in turns with the eggs on low speed, then mix in the flour. Stir in the vanilla, lemon zest, and rum until just combined.
Spread the frangipane into the cooled shell. Blot the pears on paper towels, halve them, and slice each half crosswise. Set each fanned half on the filling with the narrow end pointing to the center.
Bake at 375°F (190°C) for 40 to 55 minutes, until the filling rises around the pears and turns deep golden. Cool the tart until lukewarm or room temperature before removing the pan sides. Dust it with powdered sugar right before serving.