Preheat the oven to 350°F (175°C). Grease and flour a 9x13-inch baking dish.
In a large bowl, beat the eggs until light and foamy. Add the oil, sugar, and vanilla; mix well.
In a separate bowl, sift together the flour, salt, baking soda, and cinnamon. Gradually add the dry ingredients to the egg mixture, stirring until well combined.
Fold in the chopped apples and walnuts. Pour the batter into the prepared baking dish.
Bake for 45-50 minutes or until a toothpick inserted into the center comes out clean.
While the cake is baking, prepare the topping. In a saucepan, combine the butter, brown sugar, milk, and vanilla. Bring the mixture to a boil, stirring constantly. Boil for 1 minute.
Remove the cake from the oven and immediately pour the topping over the hot cake, spreading it evenly.
Allow the cake to cool before serving. The topping will form a delicious caramel-like layer on top of the cake as it cools.