Preheat oven to 350 degrees F. Grease and flour a 13x9 inch pan and set aside.
In a large bowl sift together flour, sugar, salt, cinnamon and soda. Make a well in the center and add oil, applesauce, eggs and vanilla mixing very well. Batter will be thick. Fold in chopped apples and nuts. Spread into the prepared pan.
Bake for 35-40 minutes, or until a toothpick inserted into cake comes out clean.
To make the glaze, heat a saucepan on medium and brown butter. When fragrant with brown bits, add brown sugar and milk. Bring to a boil and continue cooking for 2 1/2 minutes, stirring constantly. Turn off heat, then stir in vanilla. Pour over cake while still hot. Enjoy!