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

Combine pumpkin, brown sugar, applesauce, egg whites, and egg in a large mixing bowl. Beat using an electric mixer on medium speed until blended. Add flour, cocoa, baking powder, cinnamon, nutmeg, cloves, and salt. Beat on low speed until batter is smooth. Spread evenly into the prepared pan.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, 20 to 25 minutes. Remove from the oven and let cool completely in the pan on a wire rack.