In a saucepan, place the oats and the water and simmer 15 minutes to soften slightly. Allow to cool to room temperature.
Preheat the oven to 350 degrees F. Lightly butter a 8-inch square cake pan.
In a mixer fitted with a whip attachment, cream the butter until smooth. Add granulated sugar and mix until smooth and fluffy. Add the eggs and vanilla and mix just until combined. Add the cooked oats and mix just until combined.
In another bowl, mix the flour, oat bran, baking soda, cinnamon, and salt. Working in 3 batches, add the dry ingredients to the butter-oat mixture, alternating with the applesauce mixing just until combined after each addition. Pour into the prepared pan. Bake until a tester inserted into the center of the cake comes out dry and almost clean (a few crumbs are fine), 40 to 50 minutes. Let cool completely. Turn cake out onto a square serving platter. Place strips of paper under the cake around all the edges.
To make the frosting, in a mixing bowl with a whip attachment cream the cream cheese on medium to high speed until light and fluffy. Turn the mixer to low and mix in the powdered sugar and honey. Frost the cake on the sides with a thin layer of frosting then use the remaining to cover the top and swirl it decoratively. Using your hands, press the toasted chopped nuts onto the side of the cake to coat it. Remove the paper strips before serving. Cut into 2-inch square pieces.
Notes about the recipe: This is a delicious hearty and healthful cake. The texture added by the cooked steel cut oats makes you thing there are nuts inside. I made it to help me use up ends of jars of oat bran in the freezer and steel cut outs in the cereal drawer after the hot cereal breakfast season was over for the year.