Add the flour, granulated sugar, and brown sugar to a bowl. Cut the butter into small cubes, add it to the flour and sugar. Use a fork (or your fingers) to mix the butter and the flour/sugar until a crumbly mixture forms. All the butter should be incorporated with the dry ingredients.

Place it in the fridge while you make the cake batter.

Wash, peel, and chop the apples into approximately half inch cubes. Place them in a bowl, mix with cinnamon and nutmeg. Set it aside.

Pre-heat the oven to 350ºF.

Grease an 8" or 9" springform pan with butter (salted or unsalted). If using an 8" pan, make sure it's ~4-5 inches deep.

In a medium bowl, whisk together the flour, baking powder, salt, and cinnamon powder. Set it aside.

Use an electric mixer to beat the butter at medium speed for 2 minutes. You can use a stand mixer or a hand mixer.

Add the sugar and beat together with the butter for another 2 to 3 minutes, until the mixture is light and fluffy.

Scrape the bowl every so often to ensure everything is getting nicely incorporated together.

Add the eggs, one at a time, mixing until incorporated before adding the next egg.

Add the vanilla, rum, and buttermilk, then mix to combine.

Add the dry ingredient mixture and mix on low to combine. You can also use the spatula instead of the mixer to fold the batter during this final stage. Avoid over mixing, to prevent the cake from turning out dry.

Spread 2/3 of the batter on the bottom of the prepared cheesecake pan.

Top with half of the apples, enough to form an even layer of apples on top of the cake batter

Top with the remaining batter. Smooth it out gently. It’s ok if some of the apples aren’t completely covered by batter.

Pour the remaining apples on top. Spread them evenly.

Sprinkle the crumb all over the top of the cake, on an even layer.

Bake the cake in pre-heated oven for ~60-65 minutes (check at ~60 minutes). If the crumble is browning too much towards the end, and the center is not yet cooked, cover it with a piece of aluminum foil.

You will know the cake is done baking when you touch the top of the cake and doesn’t feel soft or jiggly in the center underneath the crumble layer. Also insert a toothpick in the cake, and should come out clean, without any gooey batter attached.

Let the cake cool down for about 30 min to 1 hour before drizzling with glaze or serving.

About baking: if using a convection oven bake at 325ºF. Baking time will vary depending on cake pan size and on your oven. Make sure to start checking at around 50 minutes, so you don't end up over baking the cake.

To make the glaze, beat the cream cheese, whole milk, powdered sugar, and vanilla using a hand mixer. You can also use a whisk or spatula as long as you are capable of vigorously mixing the mixture.

Add more milk as needed to thin out the glaze. Or more powdered sugar in case it becomes too runny.

Once the glaze is smooth, it’s ready. If you notice the glaze is too thick, add more milk until you are able to drizzle it over the cake.

Store the cake in a sealed container without the glaze at room temperature for up to 2 days, or up to 5 days in the fridge. If you drizzle the glaze over the cake, it may be best to store it in the fridge due to the cream cheese.

Once the cake has been stored in the fridge, it has to come to room temperature before being served.

The cake can also be stored in the freezer. Wrap it tightly with plastic wrap, and place it in an air-tight container. Store in the freezer for up to 1-2 months. Thaw in the fridge overnight, and let it come to room temperature before serving it.