For the dough: In a food processor, combine the flour, sugar, baking powder, and salt. Process just to combine. Drop in the butter pieces, and pulse until lumpy, like coarse oats or meal form. Beat the egg and almond extract together in a spouted measuring cup. With the processor running, pour in the egg. Process until the dough just comes together, adding a little more flour or cold water if it is too wet or too dry. Scrape the dough onto your work surface, and knead a few times, just to bring it together. Flatten it into a disk, and wrap it in plastic. Let it rest in the refrigerator for 1 hour.

Preheat the oven to 375 degrees. On a floured work surface, roll the dough into a ¼-inch-thick round. (If you have trouble rolling, roll the dough between two layers of parchment.) Fit the dough into an 8-or-9-inch fluted tart pan with a removable bottom. Trim off any excess or overhang. Put the shell in the freezer to firm up for 10 minutes.

Line the shell parchment and dried beans to weight it down. Bake until the dough is set and barely light golden, about 15 minutes. Cool it completely on a rack. Reduce the oven temperature to 350 degrees.

For the filling: Peel and core the apples, and cut them into ½ inch thick slices. Put the apple slices in a large bowl, and toss them with 2 tablespoons each of the apricot preserves and the sugar and all the lemon juice. Let the filling sit 10 minutes.

In a medium bowl, whisk together the vanilla, the egg, and the remaining 2 tablespoons sugar until pale yellow. Whisk in the cream and milk until smooth.

Spread the remaining 2 tablespoons apricot jam on the bottom of the cooled tart shell. Arrange the apple slices (leaving the juices behind in the bowl) over the jam in two concentric, slightly overlapping circles. Put the tart on a baking sheet, and pour the custard mixture over the apples. Bake until the custard is set and the apples are tender, about 40 minutes. Cool the tart completely on a rack. Remove tart from the pan and serve.