On a lightly floured surface, roll the dough out to a 12-inch circle, about 1/8-inch thick. Gently fit the dough into a 10-inch fluted tart pan with a removable bottom, easing the pastry gently into the bottom and sides. Trim the edges of the dough so that they slightly overhang the edge of the tart pan, then fold this excess dough over the sides so that the outer edges are almost twice as thick as the bottom of the crust. Press so that the edges are flush with the top of the pan. Cover and refrigerate for at least 30 minutes or overnight.
Preheat the oven to 350 degrees F and position a rack in the center of the oven. Line the tart shell with parchment paper and pie weights, beans or rice and bake until set and the edges just begin to firm up, about 15 minutes. Remove the parchment and weights and bake until completely set, 10 to 12 minutes. Cool completely on a wire rack.
Reduce the oven temperature to 325 degrees F.
To prepare the tart filling, combine the sugars and flour in a large bowl and stir to blend. Add the eggs, dark and light corn syrups, rum, vanilla and salt; whisk to blend.
Crumble the pralines evenly over the bottom of the prepared tart shell and pour the filling over the pralines. Bake until the tart is set, 1 hour and 10 minutes to 1 hour and 20 minutes. Cool completely on a wire rack.
To serve, cut the tart into 8 slices. Spoon about 1 1/2 tablespoons of the Caramel Sauce onto the center of 8 dessert plates and arrange the slices on top. Drizzle each slice with about 3 tablespoons of the Chocolate Sauce and arrange a scoop of Vanilla Ice Cream to the side. Serve immediately.