Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 9x13-inch pan. Mix flour, baking soda, cinnamon, and salt together in a medium bowl; set aside.

Combine eggs, oil, and sugar in a large bowl; beat with an electric mixer until lighter in color. Add flour mixture and beat well. Add vanilla and stir in chopped apples and walnuts. Pour cake batter into prepared pan.

Bake in the preheated oven until a toothpick inserted into the cake comes out clean, about 45 to 50 minutes. Allow cake to cool.

To make the frosting: Combine cream cheese, softened butter, confectioners sugar, and 1 teaspoon vanilla in a medium bowl; beat until smooth. Spread on cooled cake.