Preheat the oven to 350°F.
Lightly spray a 12-cavity muffin pan with cooking spray or line the pan with liners.
In a large mixing bowl, combine the oats, flaxmeal, baking powder, pumpkin pie spice, cinnamon, and salt. Whisk well to combine. Set aside.
In a small mixing bowl, combine the pumpkin purée, maple syrup non-dairy milk, and vanilla. Whisk well until smooth.
Pour the wet ingredients into the dry. Mix well to combine thoroughly. Be sure to scrape the bottom and sides of the bowl to incorporate fully.
Add the diced apples and mix to distribute evenly.
Fill each muffin cup all the way and press down to pack it in.
Bake for 20 to 25 minutes until oatmeal pulls away from the sides of the pan and the tops are lightly browned.
Let cool in pan for 5 to 10 minutes.
Run a knife along the edges, if needed, to help get them out. They should come out easily!