Banana Bread Pudding with Rum Toffee Sauce

Name: Banana Bread Pudding with Rum Toffee Sauce
Ingredients: 1/2 stick (4 tablespoons) unsalted butter, divided; 1 cup packed dark brown sugar; 3 large yellow bananas, mottled with brown flecks, divided; 1 teaspoon ground cinnamon; 1/2 teaspoon kosher salt; 1/4 to 1/2 teaspoon ground nutmeg; 1/4 teaspoon ground ginger (optional); 3 cups whole milk; 2 large eggs; 2 large egg yolks; 1/4 cup dark rum; 1 teaspoon vanilla extract; 1 (1-pound) loaf day-old French bread; 1 stick (4 ounces) unsalted butter; 1/2 cup packed dark brown sugar; 1/4 teaspoon kosher salt; 3 tablespoons dark rum; 1/4 cup heavy cream