Preheat oven to 375 F.
Line a 12-tin muffin pan with muffin or large cupcake liners or spray the inside with nonstick baking spray. For cinnamon sugar topping, mix together sugar, flour, butter and cinnamon. Keep it aside.
Shift together flour, baking powder, baking soda, cinnamon, and salt.
Peel and core apples (peeling is optional). Reserve 1 cup of bite-sized apples. Grate the rest of the apples manually by hand of a food processor.
Squeeze grated apple using both hands or in a colander. Discard the liquid. You should get 2 cups of tightly packed grated apples after squeezing the liquid.
In a large mixing bowl whisk together sour cream, eggs, butter, and vanilla extract to a smooth consistency.
Stir in brown sugar, chopped and grated apples to the above mixture.
Add dry ingredients mix to the wet mixture. Mix just until everything is incorporated. Don't over mix.
Use a large ice cream scoop or a spoon to fill the lined muffin liners until they are just above 3/4th filled.
Divide the cinnamon sugar topping among the muffins ( about 1 teaspoon in each).
Bake in the oven on a rack in the top third of your oven for 20 to 25 minutes, or until a cake tester comes out clean.
Remove from the baking tray and let it cool on a wired rack.