How to Make It
Preheat the oven to 425°. In a cake pan, toast the hazelnuts for 6 to 8 minutes, or until the nuts are fragrant and their skins blister. Transfer the hot nuts to a kitchen towel and rub them together to remove the skins. Let the nuts cool completely. Finely grind them in a food processor.
On a lightly floured surface, roll out the dough 1/8 inch thick. Gently ease the dough into an 11-inch fluted tart pan with a removable bottom. Line the dough with foil, leaving 2 inches of overhang. Fill the foil with pie weights or dried beans and bake for 20 minutes, or until the edges are golden and the bottom is dry. Lift out the foil and weights and bake for 5 minutes longer. Turn the oven down to 375°.
Spread the hazelnuts in the tart shell in an even layer. Arrange the plums, skin side down, in concentric circles over the nuts and sprinkle with the sugar. Bake the tart in the middle of the oven for about 35 minutes, or until the plums are tender. Brush the plums with apricot glaze and let the tart cool slightly before serving.