Strips of pate brisee woven in the style of classic chair caning give a twist to the familiar lattice-topped tart (the star pattern is easier to make than it seems). Even the filling is a surprise!
On a lightly floured surface, roll each disk of pate brisee into a 14-inch circle, 1/8 inch thick. Place 1 circle on a parchment-lined baking sheet, and freeze until firm, about 30 minutes. Fit the other circle into an 11-inch fluted round tart pan with a removable bottom. Trim dough flush with top edge of pan. Refrigerate until ready to use.
Make the lattice: Remove baking sheet from freezer. Using a clean ruler as a guide, cut dough circle into sixteen 1/2-inch-wide strips with a sharp knife or a fluted pastry wheel. Lay 6 strips of dough on another baking sheet in parallel lines that extend slightly past the width of the tart pan. Lay 6 more strips on top, almost perpendicular to the first strips. Starting in the center, weave 1 new strip diagonally through the existing grid, under the bottom layer of strips and over the top layer. Push diagonal strip into corner of each square (where the perpendicular and parallel strips meet) to create a tight fit. Weave a second strip 1 inch away, this time weaving over then under. Repeat weaving strips across 1/2 the tart. (If dough strips become too soft, return to freezer until firm.) Return to center, and repeat with remaining dough strips to form a star lattice pattern. Freeze until ready to use.
Bring water, Cognac, sugar, vanilla seeds and pod, cinnamon stick, orange zest, and cloves to a boil in a medium saucepan, stirring until sugar dissolves. Add dried fruits, reduce heat, and simmer gently until fruits soften but have not broken down, about 20 minutes. Strain through a sieve into a measuring cup, and reserve fruit and liquid separately. Let both cool. Discard vanilla pod, cinnamon stick, orange zest, and cloves. (If you have more than 2 cups liquid, simmer in a small saucepan over medium-high heat until reduced; it's fine if you have slightly less than 2 cups.)
Spread cooled fruit mixture evenly on dough in tart pan, and brush with 1/2 cup of the reserved cooking liquid. Combine yolk and cream in a small bowl, and brush some along top edges of tart. Carefully slide frozen lattice on top of tart, centering it on filling, and press edges to seal. Trim excess dough. Brush top of lattice with egg wash. Refrigerate, uncovered, until firm, about 1 hour.
Preheat oven to 400 degrees. Bake tart for 15 minutes. Reduce heat to 375 degrees, and continue baking until crust is golden brown and filling is bubbling, about 40 minutes. (If crust browns too quickly, tent edges with foil.) Brush crust and fruit with another 1/2 cup reserved cooking liquid. Let cool in pan on a wire rack. Unmold, and serve immediately with creme fraiche on the side.