Preheat oven to 325º F, grease an 8 x 8 inch baking dish with cooking spray or butter
In a large mixing bowl with an electric mixer on medium speed, combine the butter, brown sugar together, add in the maple syrup, vanilla and egg until smooth.
In a separate medium mixing bowl, whisk together the flour, baking soda and salt.
Add the dry ingredients to the wet ingredients and mix with the electric mixer until just combined, don't overmix.
Fold in the chopped walnuts.
Spread the cake batter evenly into the prepared baking dish. Bake for 40-45 minutes until a toothpick comes out clean.
Allow the cake to cool in the pan for 10-15 minutes before inverting onto a cooling rack.
Maple Frosting
In a large mixing bowl, cream together the butter and cream cheese until smooth on high speed.
Add in the brown sugar and maple syrup until well combined and smooth.
Slowly add in the powdered sugar a few tablespoons at a time until incorporated, mixing in between.
Continue mixing on high speed for about 2 minutes until the frosting is smooth.
Spread the frosting on the cooled cake and top with chopped walnuts if desired