Preheat oven to 350 degrees. Spray a 9 x 13 pan with non-stick cooking spray and set aside.
In a large bowl, beat butter, brown sugar, and eggs together with a mixer until smooth. Stir in apple sauce.
Add in flour, baking soda, salt, and pumpkin spice. Blend just until combined. Pour into the prepared 9 x 13 inch pan.
Bake at 350 degrees for 25 minutes or until a toothpick inserted in the center comes out clean. Allow to cool.
To make frosting, add cream cheese and butter to a bowl, Beat with a hand mixer until smooth. Add in powdered sugar and vanilla. Mix in until combined and fluffy. Spread over cooled cake. Serves 12-15.