Step 1: Preheat your oven to 350°F (175°C) and grease a 9×9 inch baking pan with butter or non-stick spray.
Step 2: In a medium bowl, prepare the streusel by combining the brown sugar, 1/3 cup flour, and 1 teaspoon of cinnamon. Cut in the cold cubed butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs.
Step 3: In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy. Beat in the eggs one at a time, followed by the vanilla extract and sour cream.
Step 4: In a separate bowl, whisk together the 2 cups of flour, baking powder, baking soda, salt, and the remaining 1 teaspoon of cinnamon. Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Step 5: Spread half of the cake batter into the prepared pan. Top with half of the chopped apples and half of the streusel mixture.
Step 6: Carefully spread the remaining batter over the streusel layer, then top with the remaining apples and the rest of the streusel topping.
Step 7: Bake for 45-55 minutes, or until a toothpick inserted into the center of the apple and cinnamon streusel coffee cake comes out clean.
Step 8: Allow the cake to cool in the pan for at least 20 minutes before slicing and serving.