This recipe makes two 9½-inch tart shells. Double the filling recipe or reserve the second tart shell for another use. To reserve half, of the dough wrap tightly and freeze for up to 1 month.
Preheat the oven to 350 degrees F.
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 cooled browned butter, cream, honey, and egg whites 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 flour, confectioners sugar, 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 over-mix. Turn the dough out onto the counter and divide it in two. 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 wrapped tightly and frozen for up to 1 month.
Let the dough stand at room temperature for 30 minutes to soften. Lightly butter two 9½-inch fluted tart pans with removable bottoms.
Dust a work surface lightly with flour. Dust one of the discs lightly with flour and, using a floured rolling pin, roll it out into a roughly 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. Prick the bottom of the tart shell all over with a fork. Chill the tart shell for 20 minutes. (The tart shell can be refrigerated for up to 24 hours.)
Preheat the oven to 325 degrees F. Lightly butter a pieces of aluminum foil large enough to generously line the tart pan. Line the tart shell with the foil, buttered-side down, and fill with dried beans, rice, or pie weights.
Bake the tart shell for 15 minutes. Remove the foil and beans and continue baking for 8 to 10 minutes longer, until evenly golden brown. Cool completely on a wire rack.
Melt the butter in a large skillet over medium heat and cook until golden brown and fragrant, about 5 minutes. Add the diced apples, honey, and calvados, and cook, stirring occasionally, for 2 minutes. Carefully light it with a match, and cook until the flame dies. Drain the apples in a strainer set over a bowl, reserving ¼ cup of the cooking liquid. Stir the reserved liquid back into the diced apples.
Pour the apple mixture into the tart shell and spread in an even layer. Scrape the financier batter over the apples, covering them completely.
Bake the tart until the top is golden brown and a toothpick inserted into the center comes out clean, 45 to 50 minutes. Place the tart on a wire rack.
Put the honey in a heatproof glass measure and microwave on high until hot, 10 to 15 seconds. (Or, heat in a small saucepan.) Brush the honey over the top of the hot tart. Cool the tart completely before serving.