Preheat your oven to 350°F (175°C) and prepare a 9x13-inch baking pan.
Wash and dice your apples, yielding about 2 cups.
In a bowl, whisk together baking powder, baking soda, ground cinnamon, and salt.
In a large mixing bowl, combine rolled oats, applesauce, brown sugar, granulated sugar, vegetable oil, eggs, and vanilla extract. Mix well.
Gradually add the dry mixture to the wet ingredients and stir gently until just combined.
Fold in the diced apples and optional nuts.
Pour the batter into the prepared baking pan and spread evenly.
Bake for 30-35 minutes, checking for doneness with a toothpick.
Allow the cake to cool in the pan for about 10 minutes before transferring to a wire rack.