Preheat oven to 425°F.
Roll out walnut pastry dough to an 11-inch round, or simply unroll the purchased crust. Fit into a 9-inch tart pan with removable sides or a 9-inch springform pan. If using the springform pan, roll the edge of the pie crust towards the centre of the pan until a thick edge is formed around the pan. Prick bottom of pie shell in several places. Cut brie into ¼-inch-thick slices. Lay over crust bottom, placing edge slices rind-side down. For shiny pastry, whisk egg with 2 tbsp water and brush over exposed crust.
Place in oven and immediately turn oven down to 350°F. Bake in centre of oven until pastry is golden and cheese is bubbly, about 20 minutes.
Meanwhile, trim fig stems. Slice figs in half through the stem end. Place cut-side down and slice each half into 3 wedges. When pastry shell is golden, place on a heatproof surface. Arrange figs in shell, skin-side down, in a starburst fashion. Gently brush fruit with maple syrup. Return to the 350°F oven for 10 to 15 minutes to warm figs.
Make Ahead Tip: The dough will keep, tightly wrapped in plastic wrap, in the refrigerator for up to 2 days or in the freezer for up to 6 months. Return dough to room temperature before rolling.
Walnut Pastry Dough recipe from: Davis, Suzanne. "Walnut Pastry Dough." EatingWell Magazine. September 1997.