Preheat oven to 350°F (175°C). Grease and flour a 9×13-inch baking pan.

In a medium bowl, whisk together flour, baking powder, baking soda, salt, and cinnamon. Set aside.

In a large bowl, cream together butter and sugar until light and fluffy. Add eggs one at a time, beating well after each. Mix in vanilla.

Alternately add flour mixture and sour cream (and milk) to the butter mixture, beginning and ending with flour mixture. Mix until just combined. Fold in chopped apples.

Pour batter into prepared pan and spread evenly.

For the streusel, combine flour, brown sugar, and cinnamon in a small bowl. Cut in cold butter until mixture resembles coarse crumbs. Sprinkle evenly over cake batter.

Bake for 40–45 minutes, or until a toothpick inserted into the center comes out clean.

Allow cake to cool in pan for 15 minutes before serving.