Preheat oven to 350F/177C. Butter a 10 x 6.5 inch glass pan.
Mix brown sugar and butter together until fluffy. Add the egg and vanilla and mix.
Add the flour, baking soda, cinnamon and sour cream. Mix well. Then add the apples and mix.
Pour mixture into the glass pan and spread evenly with a spatula. The mixture is quite thick so you will need to spread it out.
To make the crumb topping, mix all the ingredients until you get small "crumbs" and sprinkle evenly over the top of the wet mixture. A Kitchen Aid mixer is great for doing this but some of us aren't that lucky so I just use a fork. (Careful using your fingers to mix--the heat will make one giant crumb instead of many little ones.)
Bake for 40 minutes.