Preheat the oven to 350°F. Line an 8x8-inch baking pan with parchment paper, leaving some overhang for easy removal. Lightly grease the paper with nonstick spray and set aside.
Peel the apple, remove the core, and chop it into small bite-sized pieces; set aside.
In a large mixing bowl or the bowl of a stand mixer, beat the softened butter, granulated sugar, brown sugar, egg, and vanilla together until light, smooth, and creamy.
Add the flour, salt, baking powder, and cinnamon to the butter mixture. Mix on low speed just until combined.
Pour in the milk and mix until a smooth, thick batter forms, scraping down the sides of the bowl as needed.
Spread half of the batter evenly into the prepared pan. Scatter the chopped apples evenly over the batter.
To make the crumb topping, place the softened butter, brown sugar, flour, and cinnamon in a medium bowl. Use a pastry cutter or fork to cut the butter into the dry ingredients until the mixture forms crumbs.
Sprinkle half of the crumb mixture over the apples.
Gently spread the remaining batter over the apples and crumbs (it’s okay if some apples peek through). Top with the remaining crumb mixture.
Bake for 40-45 minutes, or until a toothpick inserted into the center comes out clean or with only a few moist crumbs.
Allow the cake to cool completely in the pan.
For the glaze, whisk together powdered sugar, vanilla, and milk until smooth. Drizzle over the cooled cake.
Serve and enjoy!