Preheat the oven to 350 degrees. Grease a 9x5 loaf tin and set aside. In a large bowl, stir together the two cups of flour, salt, cinnamon, and baking soda. Set aside.
In the bowl of a stand mixer, cream together the butter and brown sugar. Add the eggs and bananas, and stir until well combined. Pour that into the dry ingredients and stir well so all ingredients are incorporated.
Fold in the apple chunks until well dispersed. There's not really a need to coat them in flour first, because there are so many that it's unlikely they'll sink to the bottom of the loaf, but it never hurts to do so just in case.
Pour the batter into the tin and bake for about an hour, checking the loaf for doneness starting at 50 minutes. When the loaf comes out of the oven, you can either choose to cover it with syrup while hot or wait and serve it on the side, as I did here. Let cool for 30 minutes in the tin before turning out onto a serving plate, slice, and enjoy!