Preheat the oven to 350 degrees F (175 degrees C). Lightly grease and flour a 9x13-inch pan.

Sift flour, salt, cinnamon, and baking powder together; set aside.

Beat eggs and sugar together in a large bowl with an electric mixer on high speed until light in color, about 2 to 3 minutes; beat in oil until combined. Add flour mixture and mix well. Add vanilla and fold in apples and nuts. Pour cake batter into prepared pan.

Mix 4 teaspoons sugar with 1 teaspoon cinnamon in a small bowl; sprinkle over cake.

Bake in the preheated oven until a toothpick inserted into center of the cake comes out clean, about 50 to 60 minutes.