Preheat the oven to 375 degrees F. Grease and flour a standard 12-cup muffin pan.
In the bowl of a stand mixer, cream together the butter, brown sugar and granulated sugar on medium speed, for 3-4 minutes, until light and fluffy.
Add the egg and continue mixing until incorporated, scraping down the bowl once or twice (about 2 minutes). Add the sour cream and vanilla and mix on low speed another minute.
Add the flour, baking soda, baking powder, salt and cinnamon and mix on low speed just until incorporated.
Remove the bowl from the stand mixer, add the apples, and give it a good stir with a rubber spatula until the apples are evenly distributed in the batter.
Divide the muffin batter evenly between the muffin cups. They should be about 3/4 full.
Topping: In a small bowl, stir together the brown sugar and cinnamon. Sprinkle evenly over the muffins.
Bake muffins in the preheated oven for 25-30 minutes, until a toothpick inserted in the centre comes out clean.
*If you don't have sour cream on hand, you can use plain yogurt or buttermilk instead. In a pinch, you can make a homemade version of buttermilk by combining 1 tablespoon of white vinegar or lemon juice and enough milk to make a cup.