In the work bowl of a food processor, pulse together the hazelnuts and confectioners’ sugar until combined.
Add the flour, salt, cinnamon and nutmeg and pulse until combined. Add the cold butter, and pulse until mixture is crumbly.
In a small bowl, whisk together egg and 1 tablespoon water. Pour the egg mixture over the surface of the flour-hazelnut mixture in the food processor. Pulse until the dough just starts to come together but is still a little crumbly.
Reserve 1 cup (235 grams) of the hazelnut mixture for the topping. Place it in a bowl or wrap it in plastic and refrigerate until ready to use.
Pour the rest of the hazelnut mixture into a 9-inch springform pan. Place about 2 tablespoons of flour on a piece of wax paper. Pat your fingers in the flour and then press the hazelnut dough into the bottom and up the sides of the pan.
The springform pan I used is 3 1/4-inches high. Press the dough 2-inches up the side of the pan. It should be about 1/4-inch thick.
Freeze the tart shell until firm, about 1 hour. This tart shell can sit in the freezer overnight. Place the 1 cup of reserved hazelnut mixture in the refrigerator.
For the Plum Filling
Preheat oven to 375°F (190°C).
In a small bowl, combine granulated sugar and vanilla bean seeds and rub together with your fingertips. Stir in the salt and the cornstarch; set aside.
Roughly chop 1/4 cup of hazelnuts and set aside.
Cut smaller plums into quarters and larger plums into 6 pieces. Starting from the outside edge, arrange the plums on their side, in tight concentric circles. They should be tightly packed. Sprinkle the plums with the sugar-cornstarch mixture. Crumble the reserved hazelnut mixture over the plums. Sprinkle with chopped hazelnuts.
Place the pan on a rimmed baking tray (in case of leakage). Bake until the hazelnut topping is a deep golden brown and fruit is bubbly, 50 to 60 minutes. Cover the pan with foil to prevent excess browning, if necessary.
Remove the tart from the oven and let it cool completely in the pan. Remove the ring and serve at room temperature with ice cream or whipped cream.
Notes
Adapted from the Bake Feed recipe for Apricot and Hazelnut Crumb Tart