Combine & whisk 1 & 1/2 cups flour and 1 & 3/4 teaspoons baking powder together in another bowl and set aside.
In another medium-sized bowl, beat 2/3 cup sugar and 1/2 cup softened butter together using an electric mixer until smooth and creamy.
Beat in applesauce or flax eggs until blended in; add in 1 & 1/2 teaspoons vanilla extract and mix in until combined. Will not be completely smooth, that's fine.
Add the flour mixture into creamed butter mixture and mix until blended.
Mix 1/2 cup milk into batter and continue mixing until smooth.
Using a small cookie scoop or large spoon, scoop or spoon some batter into 11 of the prepared muffin tins; add some of the chopped apple mixture with the sugar and cinnamon added in to each muffin.
Then sprinkle a teaspoon or two of the brown sugar/cinnamon mixture on top of apple layer.
Repeat all the layers again. Can swirl the mixture with a knife if you wish for swirl effect if you wish.
Bake in the preheated oven until a toothpick inserted in the center of the muffin comes out clean, approximately 20-25 minutes.