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

Whisk together flour, cocoa powder, baking soda, and salt in a medium bowl.

Beat butter and sugar together in a large bowl with an electric mixer on medium speed until light and fluffy. Beat in eggs, one at a time, then beat in vanilla extract.

Add flour mixture alternately with applesauce, beginning and ending with the flour mixture. Beat just until combined. Spread batter evenly in the prepared pan. Sprinkle with chocolate chips and walnuts.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 35 minutes. Let cake cool completely in the pan on a wire rack before serving.