Preheat oven to 350 degrees F and butter and flour a 9-x-5" loaf pan.
In a large bowl, whisk together 1 cup flour, baking soda, and salt.
In another large bowl, combine ¾ cup sugar, ½ cup butter, buttermilk, vanilla, egg and egg yolk until smooth. Pour wet ingredients over dry and stir until combined, then fold in strawberries and mashed bananas.
Make crumb topping: Combine remaining ½ cup flour, remaining ¼ cup sugar, remaining ½ cup butter, and a pinch of salt.
Transfer batter to prepared baking dish and top with crumb topping. Bake until deeply golden and a toothpick comes out clean, about 60 minutes. Let cool at least 10 minutes before serving.
To serve as a shortcake, stack banana bread with freshly whipped cream and strawberries.
