Preheat your oven to 350 degrees F. Grease and flour a 9-inch square baking pan.
In a medium bowl, whisk together 1 3/4 cups flour, baking powder, salt, and 1 teaspoon cinnamon. Set aside.
In a large bowl, beat the softened butter and granulated sugar with an electric mixer until light and fluffy.
Beat in the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, alternating with the milk, beginning and ending with the dry mixture. Mix until just combined. Do not overmix.
Fold in the diced apples gently. Pour the batter into the prepared pan and spread evenly.
Prepare the crumb topping: In a separate bowl, combine the cold butter pieces, brown sugar, 1 1/2 cups flour, and 1 teaspoon cinnamon. Use your fingers or a pastry blender to cut the butter into the dry ingredients until coarse, pea-sized crumbs form.
Sprinkle the crumb mixture evenly over the cake batter.
Bake for 50 to 60 minutes, or until a wooden pick inserted into the center of the cake (avoiding the thickest part of the topping) comes out clean.
Let the cake cool in the pan for 15 minutes before transferring it to a wire rack to cool completely.
If using the drizzle, whisk together powdered sugar, milk, and cinnamon until smooth. Drizzle over the cooled cake before serving.
Notes
For a moister cake, use Granny Smith or Honeycrisp apples.
You can substitute sour cream for the milk for an even richer texture.
If you prefer a thicker topping, increase the topping flour to 1 3/4 cups.