Step 1Set a rack in the center of the oven; heat the oven to 425 degrees. Set aside a greased 8 1/2-inch diameter tart pan with a removable bottom.
Step 2Pulse together the flour, sugar and salt in a food processor once or twice to mix. Scatter the shortening and butter over the flour. Pulse on/off until the mixture is cut into small bits. Drizzle the yolk-water mixture over the top. Pulse on/off until the pastry is uniformly crumbed, about 10 seconds.
Step 3Transfer the crumbs to the pan. Spread the crumbs in the pan with more around the rim. Through plastic, press the crumbs up onto the sides. Then, press the crumbs into the bottom. Use your finger to even out the thickness at the edge of the pan. Refrigerate the pastry until well chilled, about 1 to 2 hours. Cut a piece of parchment or foil to fit the pan with a slight overhang. Gently conform it to the pan. Fill the pan with dried beans, raw rice or pie weights to weight down the pastry.
Step 4Bake until the edges are set, about 10 minutes. Carefully remove the paper and beans. Bake the pastry until the edges are lightly browned, about 10 minutes longer. Set it aside to cool slightly. Reduce the oven to 325 degrees. Before filling, brush the yolk on the bottom surface to seal.
Step 1Heat the oven to 350 degrees. Spread the nuts in a single layer on a baking sheet. Toast until lightly browned and fragrant, about 15 minutes, watching carefully so they do not burn. Set them aside.
Step 2Mix the eggs on medium-low speed until light-colored and thick. Mix in the brown sugar, syrup, flour, cinnamon, cloves and salt until well combined. On low speed, slowly pour in the butter and vanilla. Stir in the walnuts. Pour the filling into the crust.
Step 3Bake the tart until the top is lightly browned, slightly puffed and the filling no longer jiggles when gently shaken, about 30 minutes. Set the tart aside on a rack to cool completely. Refrigerate at least 6 hours or overnight.
Step 4To serve, remove the tart from the pan. Cut the chilled tart into wedges. Serve immediately.