Add the butter to a large skillet over medium heat and allow it to melt.

Add the diced apples, brown sugar, and cinnamon. Cook for about 6–8 minutes, stirring occasionally, until the apples begin to soften and the sugar creates a syrupy coating.

Remove from the heat and stir in the vanilla. Set aside to cool slightly while you prepare the cake batter.

Preheat the oven to 350°F (177°C). Grease an 9x9 inch baking pan and line with parchment paper, leaving a slight overhang for easy removal.

In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg.

In a large mixing bowl, whisk together the melted butter, brown sugar, and granulated sugar until combined.

Add the eggs, vanilla, sour cream, and milk. Whisk until smooth.

Add the dry ingredients to the wet ingredients and gently stir with a spatula just until combined.

Fold about two-thirds of the cinnamon apples into the cake batter, including some of the juices from the pan.

Spread the batter evenly into the prepared baking pan. Spoon the remaining apples and juices evenly over the top.

In a small bowl, combine the 2 tablespoons brown sugar and ½ teaspoon cinnamon. Sprinkle evenly over the cake.

Bake for 45–55 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.

Allow the cake to cool in the pan for about 20 minutes before adding the glaze.

In a small bowl, whisk together the powdered sugar, milk, and vanilla until smooth. Add a little more milk as needed until the glaze is thin enough to drizzle.

Drizzle the glaze generously over the slightly warm cake. Let the glaze set for about 10 minutes before slicing and serving.