Place figs in a heatproof bowl with boiling water to cover; let stand 20 minutes or until plump. Drain figs, and slice.
Place bread and walnuts in a 15- x 10-inch jellyroll pan; bake at 500° for 3 to 4 minutes or until toasted. Remove from oven, and set aside. Reduce heat to 350°.
Heat milk, cream, and 3/4 cup sugar in a medium saucepan over medium heat. (Do not boil.)
Whisk together eggs and next 4 ingredients in a large bowl; slowly whisk in milk mixture.
Layer half of bread and walnuts evenly in a lightly greased 11- x 7-inch baking dish or 10-inch pieplate, slightly overlapping slices; layer half of figs evenly over bread. Pour half of milk mixture evenly over figs. Repeat procedure with remaining bread, figs, and milk mixture. Press lightly with a spatula. Sprinkle walnuts and remaining 1/4 cup sugar evenly over top.
Cover loosely with foil, leaving corners uncovered to brown edges (if using a pieplate, loosely cover with foil, allowing edges to brown).
Bake at 350° for 45 minutes, or until set. Remove foil, and bake 15 more minutes. Serve pudding warm with Rum Sauce, if desired.