Preheat the oven to 350°F/175°C. Line muffin tins with liners.
Mix flax meal and water; set aside to thicken for 10-15 minutes.
Prepare the topping by combining oats, brown sugar, melted butter, and cinnamon. Set aside.
In a large bowl, blend oil, applesauce, milk, vanilla, apple cider vinegar, and both sugars until well combined.
In another bowl, mix flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
Stir flax eggs into the wet ingredients. Add the dry mixture, then fold in apples and walnuts.
Scoop batter into liners, filling just over ¾ full. Top each muffin with oat topping.
Bake for 25-27 minutes, or until a toothpick comes out clean.