Preparation

Make the dough

• Break the egg into a small bowl and set aside. Combine the all-purpose and whole-wheat pastry flours, sugar, salt, and baking powder in a mixing bowl with high sides or the bowl of a stand mixer. Add the butter cubes and toss with the dry ingredients. Put the bowl in the refrigerator to chill for at least 10 minutes.
• Pour 1⁄4 cup of water over ice. Cut the butter into the dry ingredients using a stand mixer fitted with the paddle attachment or by rubbing the flour and butter together with your fingers. When the mixture resembles coarse cornmeal, add the ice water and egg, mixing just until the dough begins to come together. Turn the dough out onto a sheet of plastic wrap and use the heels and sides of your palms to gather and press the dough into a 1-1⁄2-inch-tall disk. Wrap tightly and refrigerate for at least 2 hours.

Make the filling

• Heat the oven to 325°F. Toast the hazelnuts on a baking sheet for 20 to 30 minutes, or until they are a rich dark brown and their skins are beginning to fall off. Allow them to cool slightly and then use a clean, dry dishtowel to rub the nuts together to remove the remaining skin. Set the nuts aside.
• Melt the honey, brown sugar, and butter together in a saucepan with high sides over medium-high heat. Bring the mixture to a hard boil, remove from the heat, and slowly and carefully whisk in the cream. Whisk in the eggs and vanilla when the caramel is just barely warm.

Make the tart

• Lightly flour a work surface. Roll the dough out a 14- to 15-inch circle about 1⁄4 inch thick. Fold it in half and carefully lay the dough in a 10-inch tart pan with a false bottom and fluted edges. Press the dough into the corners and up the sides of the pan, then trim the edges with a rolling pin. Refrigerate for 15 minutes and heat the oven to 350°F.
• Line the chilled tart shell with parchment paper and fill it with dried beans, rice, or pie weights. Bake for 25 minutes. Remove from the oven, reduce the heat to 325°F, and cover the bottom of the crust with the toasted hazelnuts. Pour the custard over the top and bake for 25 to 30 minutes, or until the custard has just set. Cool completely before serving and top with whipped cream if you’d like.