Makes 8 individual tarts.
For the pastry, beat the butter and icing sugar together until smooth. Push the hard-boiled egg yolk through a sieve and add this to the butter along with the raw egg yolk and vanilla. Add this to the butter mixture and stir until blended. Add the flour and salt to the butter mixture and stir until blended. Shape the dough into a cylinder (it will be very soft), wrap in plastic and chill until firm, about 2 hours.
Unwrap the chilled dough and slice it into 8 pieces. On a lightly floured work surface, roll out each piece into a circle that is just under 1/4-inch (6 mm) thick and line eight ungreased 4-inch (10 cm) removable bottom fluted tart shells with each piece of pastry, pressing the dough into the shell and trimming away excess dough. Chill the tart shells for 30 minutes or until firm.
Preheat the oven to 325°F (160°C). Place the tart shells on a baking tray, dock the bottoms of each shell with a fork and bake them for about 18 minutes, until the edges begin to brown a little. Cool the shells before filling.
For the pudding, first make a butter caramel by placing the water and lemon juice in a medium saucepan and measure the sugar over top. Bring this to a boil over high heat without stirring and continue to boil, occasionally brushing the sides of the pot with cool water, until it turns a light amber colour (or if you like an intense caramel taste, let it go until a deeper amber). Remove the pot from the heat and carefully (watching out for steam) but quickly whisk in the butter until smooth. Whisk in the vanilla and salt. You may find the butter separates out as the caramel sits, but once cooled, it can be whisked back in and will remain blended.
In another medium pot, whisk the brown sugar and cornstarch. Whisk in 2 cups (500 mL)of the milk, and have a bowl with the egg yolks ready, whisking the remaining ¼ cup (60 mL) of milk into them. Whisk the butter caramel into the egg yolks and set aside. Bring the pot with milk and sugar up to a full simmer on medium heat, whisking constantly (but vigorously is not necessary) until the mixture bubbles and has thickened. Slowly pour the pudding into the egg yolk mixture while constantly whisking the yolks, until at least half of the hot pudding has been mixed in (you can add all if you wish). Transfer the whole mixture back to the pot and continuing whisking on medium heat until bubbles just begin to break the surface. Pour the pudding through a strainer into a bowl and cover the surface of the pudding with plastic wrap. Cool for an hour and then chill completely, at least 2 hours.
To assemble, whisk the chilled pudding a little and spoon this into the cooled tart shells. Preheat the oven to 400°F (200°C).
Whip the egg whites and cream of tartar using electric beaters or in a stand mixer fitted with the whip attachment on high speed until foamy. Stir the granulated and icing sugars together and pour these into the whites while whipping and continue to whip until the whites hold a medium peak when the beaters are lifted. Dollop the meringue onto each tart and bake for about 5 minutes, until lightly browned. Let the tarts cool on a rack and then chill until ready to serve.
The tarts are best enjoyed that day they are assembled, although the crust and filling can be prepared a day or two ahead.