Preheat the oven to 350°F (175°C) and prepare a 9x13-inch baking pan.

In a large mixing bowl, combine applesauce, brown sugar, granulated sugar, vegetable oil, eggs, and vanilla extract. Mix until smooth.

In a separate bowl, whisk together flour, cocoa powder, baking soda, salt, and ground cinnamon.

Gradually add the dry mixture to the wet ingredients, stirring gently until just combined.

Fold in diced apples and chopped nuts, aiming for even distribution.

Transfer the batter to the prepared baking pan and spread evenly.

Bake for 25-30 minutes, or until a toothpick inserted comes out with a few moist crumbs.

Cool the brownies in the pan for 10 minutes, then transfer to a wire rack.

Slice into squares and serve, optionally with vanilla ice cream.