Cook 1 cup unsalted butter in saucepan until browned, about 6-8 minutes. Pour into large mixing bowl and cool for 15 minutes.
STEP 2
In a large bowl, combine apples and 1 tablespoon lemon juice. Add 1/2 cup brown sugar and 1 teaspoon cinnamon. Toss to coat and set aside.
STEP 3
Preheat oven to 350 degrees F. Generously butter a 9x13-inch baking dish.
STEP 4
To the cooled brown butter, add white sugar, remaining 1/2 cup brown sugar, 1 teaspoon salt, and 1/2 teaspoon cinnamon. Whisk together, then add eggs and vanilla. Whisk in sour cream and apple cider. Stir in flour, baking powder, and baking soda until mostly smooth.
STEP 5
Pour batter into the prepared pan. Scatter apples and juices evenly on top.
STEP 6
Bake for 55-65 minutes until a toothpick comes out mostly clean. Let cool for 15-20 minutes.
STEP 7
For icing, whisk together powdered sugar, salt, vanilla, and heavy cream until smooth. Pour over warm cake and serve.