Make toffee sauce: Melt butter in a medium saucepan. Whisk in whipping cream, brown sugar, and molasses. Cook at a low boil, whisking occasionally, until dark reddish-brown, 7 to 8 minutes. Stir in vanilla and salt and set aside.
Preheat oven to 325° with a rack in the center.
Make pudding: Bring 11/4 cups water to a boil in a small saucepan. Remove from heat and stir in 1 tsp. baking soda; then stir in dates. Let cool.
In a medium bowl, whisk 11/2 cups flour with remaining 2 tsp. baking soda and the salt; set aside. Butter bottom of an 8-in. square baking pan and line with a piece of parchment paper cut to fit, smoothing out wrinkles. Butter and flour pan, including parchment. Cover bottom evenly with walnuts, rounded sides down; then pour 3/4 cup Dark Toffee Sauce evenly over nuts to barely coat.
Meanwhile, in a stand mixer with the paddle attachment, cream 5 tbsp. butter and the sugar on medium speed until light and fluffy, about 4 minutes. Dissolve espresso in vanilla, then beat into bowl along with eggs. Reduce speed to low and, in 2 batches, beat in flour mixture. Stir in date mixture (with liquid). Pour batter into pan.
Bake cake until a skewer inserted in center emerges with a few crumbs sticking, about 45 minutes. (It will look very dark when done.) Let cool 15 minutes in pan on a wire rack, then invert onto a rimmed platter. Peel off parchment and let cool at least 15 minutes more.
Cut cake into squares and serve with remaining Dark Toffee Sauce, for drizzling.