Preheat the oven to 400°F and line a muffin tin with liners or lightly grease it.
In a large bowl, whisk together the flour, baking powder, baking soda, and cinnamon until well combined.
In a separate medium bowl, whisk together the applesauce, eggs, oil, and vanilla until smooth. Add the wet ingredients to the dry ingredients and gently stir until just combined, stopping as soon as no dry spots remain.
Fold in the chopped apple pieces evenly throughout the batter. The apples will soften during baking, but you can also grate the apple if you prefer.
Scoop the batter into the prepared muffin tin, filling each cup about three-quarters full.
Bake for 5 minutes at 400℉, then reduce heat to 350℉ and bake for 15-18 more minutes, until the muffins are set in the centre and a toothpick inserted comes out clean.
Let the muffins cool in the pan for a few minutes before transferring them to a wire rack to cool completely.