Melt the butter in a large skillet over medium heat. When the butter starts to bubble, add the apples. Sprinkle the sugar and cinnamon over the apples and cook, stirring occasionally until the apples release their juices and start to become tender, about 5-7 minutes. Remove from heat and set aside to cool to room temperature.

Drain the cooled apples, reserving the juice for the icing.

Preheat the oven to 350ºF (180ºC). Grease an 8-inch square baking dish. (I used a ceramic baking dish.*)

In a medium-size bowl, whisk together the flour, cinnamon, baking soda, salt and nutmeg until well combined.

In large bowl, beat the butter, granulated sugar and brown sugar together until light and fluffy. Beat in the egg until incorporated, then beat in the vanilla extract.

Stir in the flour mixture in 2 additions, followed by half of the sour cream after each addition. Mix just until combined. Do not over mix. Fold in the cooled, drained apples.

Transfer the batter to the baking dish. Smooth the top with a spatula. Bake until the cake is golden brown and springs back when lightly touched. A toothpick inserted into the center of the cake will be clean or have a few moist crumbs attached, about 23-28 minutes. Do not over bake.

In a small light-colored saucepan over medium heat, melt the butter and cook until it's deep golden and fragrant. When brown specks start to appear, remove it from the heat and immediately transfer it to a small bowl. Set aside to cool to room temperature.

In a medium bowl, mix the cooled brown butter with the powdered sugar, reserved apple juice, 1 tablespoon (15ml) of milk and the salt until well combined. Add additional milk as needed to achieve the desired consistency. Whisk until smooth. Spread the icing over the cooled cake.