Preheat oven to 350 degrees F. Grease and lightly flour an 8x8 cake pan. Set aside.
Cook the white beans until soft and drain well. If using canned, drain well. Set aside.
Combine the cooked beans, avocado oil, applesauce and water in a food processor or blender. Blend until smooth. Set aside.
In a medium large mixing bowl, combine the spelt flour and baking powder. Sift the carob and cocoa into the bowl and whisk well to mix.
Add the bean mixture to the bowl. Add the chopped walnuts and stir until just mixed.
Spoon batter into the prepared cake pan. Lightly smooth the top.
Bake for 18 minutes. Remove and test by inserting a tester into the centre of the cake. If it comes out clean, it's done.
Let cake cool in the pan for a minute or two. Flip cake onto a plate and then onto a baking rack.
Let brownies cool completely and cut into squares.