In a medium bowl, whisk the egg yolks and sugar until pale and thick. Whisk in the flour, salt and 1 tablespoon of the milk. In a medium saucepan, bring the remaining milk just to a simmer. Gradually whisk the hot milk into the egg mixture.
Scrape the mixture into the saucepan and bring to a boil, whisking constantly. Cook for 2 minutes. Scrape the pastry cream into a small bowl and stir in the vanilla. Press a piece of plastic wrap directly onto the surface of the pastry cream and let cool completely.
Preheat the oven to 425°. On a lightly floured surface, roll out the dough 1/8 inch thick. Gently ease the dough into an 11-inch fluted tart pan with a removable bottom, preferably not a dark pan. Trim any overhanging dough flush with the rim. Prick the bottom several times with a fork and refrigerate until firm, about 10 minutes.
Line the dough with foil, leaving 2 inches of overhang, and fill the pan with pie weights or dried beans. Bake the tart shell in the middle of the oven for 12 minutes, or until barely set and pale golden. Lift out the foil and weights and bake for 5 minutes longer, or until the shell is lightly browned and dry to the touch but not cooked through. Let cool.
Peel and halve the pears. Using a melon baller, scoop out the cores. Rub the pears with the cut side of the lemon to prevent discoloration. Thinly slice each pear half crosswise, keeping the halves intact. Using the palm of your hand, press the cut pears slightly to fan them out.
In a medium bowl, beat the butter until smooth and creamy. Add the confectioners' sugar, ground almonds, cornstarch, rum and the cooled pastry cream and beat until smooth. Add the egg and beat until blended.
Spread the almond cream in the tart shell. Using a long metal spatula, arrange the sliced pears in a radiating pattern over the cream, keeping the halves intact. Sprinkle the tart with the granulated sugar and bake until the almond cream is browned and set, the pears are tender and just beginning to brown and the crust is golden, about 40 minutes.
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