Preheat the oven to 350°F (175°C). Lightly grease a 9-inch cake pan and line the bottom with parchment paper. The parchment will make it much easier to lift the cake out once it has cooled.

Add the flour, cocoa powder, baking soda, and salt to a medium bowl. Whisk everything together until well blended, breaking up any cocoa lumps as you go.

In a large bowl, whisk the applesauce, sugar, melted butter, eggs, and vanilla until smooth. Gradually add the dry mixture and stir gently with a spatula until just combined. Stop mixing as soon as you no longer see dry flour to keep the cake tender.

Gently fold the chocolate chips and chopped walnuts or pecans into the batter. Spread the batter evenly in the prepared pan and smooth the top with a spatula.

Bake for 35–40 minutes, checking the center with a toothpick near the end of the baking time. The cake is ready when the toothpick comes out with a few moist crumbs attached. Let it rest in the pan for about 15 minutes, then move it to a wire rack and allow it to cool completely before cutting.