Wash, clean, and pat dry apples. Peel, core, and chop them. Squeeze some lemon juice to prevent from browning. In a saucepan over medium heat, melt the butter. Add chopped apples and cook, constantly stirring, until tender, for about 7 minutes. Add in brown sugar and ground cinnamon. Gently mix ingredients and cook for 5 minutes more until the sugar has dissolved. Set aside to cool.
Preheat the oven to 350° F.
Grease a baking dish with butter. In a baking dish, arrange a layer of bread cubes, then top with half of the apple mixture in an even layer. Spread the cream cheese evenly on the top. Repeat one more layer.
In a large mixing bowl, beat together eggs, milk, maple syrup, vanilla, salt, and ground cinnamon. Pour the egg mixture evenly over the casserole. Sprinkle with almond flakes generously.
Send cinnamon apple casserole to the oven for 45 minutes. Bake until golden brown and the center is firm.
Serve cinnamon apple casserole topped with vanilla ice cream.