On a floured surface, roll out the pastry to an approximate circle and transfer to a flat baking sheet. Roll up the edges to form a rim and use a fork to crimp all the way around. Prick surface of the pastry at regular intervals with the tip of the fork. Refrigerate while preparing remaining ingredients.
Drain syrup from figs and reserve syrup. Slice figs in half from stem to bottom and set aside. Place syrup in a small saucepot with half of the amaretto and let simmer over medium heat for 12-15 minutes, or until slightly thickened. Set aside. In a mixer, combine the mascarpone, goat cheese, sugar and remaining amaretto. Use a mixing paddle to blend evenly. Once blended, spread the mixture evenly to cover the bottom of the tart within 1/2-inch of the edge. Cover completely with figs (with the figs touching each other).
Sprinkle with sugar and bake for 40 minutes (until golden on edges). Remove from oven. Heat the fig and amaretto syrup in a small saucepot. Thin with water if needed. Using a pastry brush, spread mixture over entire top of the tart, coating evenly. Dust with crushed nuts. Divide tart into fourths, then each fourth into thirds, making 12 slices. Serve each slice individually with vanilla ice cream (or crème chantilly) drizzled with the amaretto-fig syrup or pecan-maple syrup.