Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan, ensuring it is well-coated.

In a medium bowl, combine 1 cup flour, 1/2 cup brown sugar, and 1 tsp cinnamon. Add the cold, cubed butter and use a pastry cutter to blend until the mixture resembles coarse crumbs. Set aside.

In a large mixing bowl, using an electric mixer, cream together 1/2 cup softened butter and 1 cup granulated sugar until light and fluffy.

Beat in the eggs one at a time, mixing well after each addition. Stir in 1 tsp vanilla extract.

In a separate bowl, whisk together 2 cups flour, 1 tsp baking powder, 1/2 tsp baking soda, 1/2 tsp salt, and 1 tsp cinnamon.

Gradually add the dry ingredients to the creamed mixture alternately with 1/2 cup milk, beginning and ending with the dry ingredients. Mix until just combined.

Gently fold in 2 cups of peeled and diced apples, ensuring they are evenly distributed throughout the batter.

Pour the batter into the prepared cake pan. Sprinkle the crumb topping evenly over the batter, pressing it down gently with your hands.

Bake in the preheated oven for 50 to 55 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow the cake to cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.

Slice the cake into 8 portions and serve warm or at room temperature. It pairs beautifully with a scoop of vanilla ice cream or a dollop of whipped cream.

Store any leftover cake in an airtight container at room temperature for up to 3 days. For longer storage, refrigerate the cake for up to a week.