Make the financier batter: Preheat the oven to 350 degrees Fahrenheit. 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 three 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 whist 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.
Make the apple filling: Melt the butter in a large skillet over medium heat and cook until it is golden brown and fragment, about five minutes. Add to the diced apples and honey and cook, stirring occasionally, for two 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 40 to 50 minutes, until the top is golden brown and toothpick inserted into the center comes out clean. Place the tart on a wire rack.
Glaze the tart: 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.
Recipe courtesy of Francois Payard, Executive Pastry Chef, Payard Patisserie