Heat the oven to 350°F (175°C). Line a 9-by-13-inch metal baking pan with parchment, covering the bottom and sides.

In a large bowl, whisk the flour, granulated sugar, baking powder and salt. In a second bowl, whisk the 1 cup milk, eggs, vanilla and melted butter until blended. The butter should be warm, not hot.

Pour the wet mixture into the dry ingredients and fold with a spatula just until the flour disappears. Fold in the small-diced apples. The batter will be thick and spreadable; avoid beating it smooth.

Stir the brown sugar and cinnamon together in a small bowl. Spread half the batter in the lined pan. Scatter half the cinnamon sugar over it, then gently spread on the remaining batter and sprinkle with the remaining cinnamon sugar. Draw a butter knife through the batter in a few wide curves, without scraping the parchment.

Bake on the center rack for 40–45 minutes. The top should be golden and a toothpick inserted into cake near the center, avoiding an apple piece, should show a few moist crumbs but no liquid batter. If needed, bake in 5-minute increments and check again.

Set the pan on a wire rack and cool for 20 minutes. Whisk the powdered sugar and 2 tablespoons milk in the cleaned small bowl until smooth. Drizzle over the warm cake. Let the glaze settle before cutting into 12 squares; cool longer for neater slices.