Gâteau Basque

In a medium bowl, whisk the flour with the baking powder and salt. In a standing mixer fitted with a paddle, beat the butter with the sugar at medium speed until light and fluffy, about 3 minutes. Add the egg yolks to the mixing bowl along with the whole eggs, lemon oil and almond oil. Beat until they are thoroughly incorporated. At low speed, gradually beat in the flour mixture and the almond flour.

Scrape the pastry dough out onto a work surface and form it into 3 disks. Wrap each disk in plastic wrap and refrigerate until very firm, at least 4 hours or overnight.

In a medium saucepan, bring the milk to a simmer over moderate heat with the vanilla seeds. In a medium heatproof bowl, whisk the cornstarch with the sugar and flour. Whisk the hot milk into the cornstarch mixture, then pour the mixture into the saucepan and cook over moderate heat, whisking constantly, until the mixture is bubbling and very thick, about 5 minutes. Add the egg yolks and the whole eggs and simmer, whisking, for 3 minutes longer. Scrape the pastry cream into a large, heatproof bowl and press a piece of plastic wrap directly onto the surface. Let the pastry cream cool to room temperature, about 30 minutes.

Preheat the oven to 350°. On a lightly floured work surface, roll out the first disk of dough to a 1/4-inch thickness and cut out a 12-inch round. Slide the round onto a lightly floured baking sheet and refrigerate until firm, about 10 minutes.

Meanwhile, roll the second disk out to a 1/4-inch thickness, and cut out a second 12-inch round. Transfer it to a 9-inch fluted tart pan with a removable bottom. Lightly press the dough onto the bottom and up the side of the pan. Trim off the excess and refrigerate the tart shell until firm, about 10 minutes. The third disk, along with any other excess dough, can be made into cookies (see Note).

Spread the pastry cream in the tart shell in an even layer and dot with the brandied cherries. Cover the tart with the first round of dough and press gently to seal the edges. Trim off any excess. Brush the tart with the egg wash. Using a fork or skewer, lightly score the top of the tart in a diamond pattern.

Set the tart on a baking sheet and bake on the bottom shelf of the oven for 20 minutes. Rotate the tart and transfer it to the upper third of the oven. Bake the tart for about 40 minutes longer, until golden brown on top. Transfer the tart to a large wire rack to cool. Serve warm or at room temperature, cut into wedges.

pure lemon oil, cold-pressed from lemon rinds, is available at specialty-food shops and online at boyajianinc.com.

Excess dough can be made into cookies: Roll the dough out to a 1/4-inch thickness. using a sharp knife, cut the dough into 3-inch squares. Brush the squares with egg wash, score them with a fork and bake for 20 minutes in a 350° oven until golden.