A financier is usually a petit four, made of an almond batter with egg whites and browned butter. This full-size financier was developed by Hervé Poussot, my friend and colleague, to take advantage of the amazing apples that are available in the fall. Consider it a French version of apple pie, but serve it without the ice cream. The moisture of the mix and the texture of the apples with the flavor of the browned butter make this delicious on its own. (We don’t decorate with fresh apples, because they turn brown, and then the tart doesn’t look nice.) This tart will keep for a week in the refrigerator.
Preheat the oven to 350 degrees.
Melt the butter in a small skillet over medium heat. Reduce the heat to medium-low and cook the butter until it begins to brown and has a nutty fragrance, about 3 minutes. Set aside to cool.
Put the slivered almonds in a food processor and process until finely ground, about 45 seconds. Transfer the ground almonds to a medium bowl. Sift the confectioners’ sugar over the almonds. Add the flour, cornstarch, and salt and gently whisk to combine.
Combine the egg whites, honey, cooled browned butter, and cream in another medium bowl. Scrape the seeds from the vanilla bean (reserve the pod for another use) into the bowl and whisk to combine. Add the dry ingredients and whisk just until combined. Set aside.
Sift together the confectioners’ sugar, flour, and salt into a bowl.
Place the butter in a food processor and process until smooth, about 15 seconds. Scatter the flour mixture over the butter, add the egg, and process just until the dough forms a mass; do not overmix. Turn the dough out onto the counter and divide it in 2. Shape each half into a disc, wrap in plastic wrap, and refrigerate for at least 2 hours or up to 24 hours. Half of the dough may be well wrapped and frozen for up to 1 month.
Let the dough stand at room temperature for 30 minutes to soften. Lightly butter two 9 1⁄2-inch fluted tart pans with removable bottoms.
Dust a work surface lightly with flour. Dust 1 of the discs lightly with flour and, using a floured rolling pin, roll it out into a rough 12-inch circle. Lift the dough often, making sure that the work surface and dough are lightly floured at all times. Roll the dough up onto the rolling pin and gently unroll it over one of the prepared tart pans. Press the dough into the pan and roll the pin over the top of the pan to remove the excess dough. Repeat with the remaining dough and tart pan. Prick the bottom of the tart shells all over with a fork. Chill the tart shells for 20 minutes. (The tart shells can be refrigerated for up to 24 hours.)
Melt the butter in a large skillet over medium heat and cook until it is golden brown and fragrant, about 5 minutes. Add the diced apples and honey and cook, stirring occasionally, for 2 minutes, or until the apples are slightly softened. Add the Calvados to the skillet, carefully light it with a match, and cook until the flame dies. Drain the apples in a strainer set over a bowl, reserving 1/4 cup of the liquid. Stir the reserved liquid back into the diced apples.
Pour the apple mixture into the tart shell and spread it into an even layer. Scrape the financier batter over the apples, covering them completely.
Bake the tart for 45 to 50 minutes, until the top is golden brown and a toothpick inserted into the center comes out clean. Place the tart on a wire rack.
Put the honey in a heatproof glass measure and microwave on high for 10 to 15 seconds, until hot. (Or, heat in a small saucepan.) Brush the honey over the top of the hot tart. Cool the tart completely before serving