Preheat the oven to 375°F (190°C) and grease or line a muffin tin with paper liners.
In a large mixing bowl, combine the rolled oats, baking powder, cinnamon, and salt. Mix well to combine.
In another bowl, whisk together the applesauce, eggs, milk, vanilla extract, and maple syrup (if using) until well blended.
Pour the wet mixture into the dry ingredients and stir until just combined.
Gently fold in the diced apple and chopped nuts (if using).
Spoon the oatmeal mixture into the prepared muffin tin, filling each cup about ¾ full.
Bake in the preheated oven for 20-25 minutes, or until the tops are lightly golden and a toothpick inserted into the center comes out clean.
Allow the oatmeal cups to cool in the pan for a few minutes before transferring them to a wire rack to cool completely.