Start by preheating your oven to 375 degrees. Line a muffin tin with 12 liners or grease well and set it aside.
Get your stand mixer fitted with the paddle attachment or a large bowl and a hand electric mixer. Add the sugar and oil in the bowl, and let mix on medium for about 1 minute. Add your baking powder, baking soda, salt, vanilla, cinnamon, nutmeg, and vinegar, and stir until well combined. Now add your flax egg and stir until combined. Add the flour and applesauce, stir until mixed, and fold in the apples.
This batter is very thick and weird. Take a large cookie scoop and scoop your apple muffin batter into the 12 cups evenly.
Take a small bowl and combine your topping ingredients cutting in the vegan butter with a fork or pastry cutter until you have small crumbs for the topping. Top each muffin with an even amount of topping.
Bake in the preheated oven for 18-22 minutes. Mine were done at 19 minutes, don't over bake.