Apple Cake for a Birthday?

It's my partner Cormac's birthday. He's turning 21, again, of course ;). He requested an "apple pie or cake thingy whatever". So, I figured as long as I used up the apples in the kitchen I'd be fine.

Apple Cake with Oatmeal Crumble
adapted from The Knead for Bread Apple Tart Bread

Ingredients

Cake
1 1/2 cups all purpose flour
1 1/2 tsp baking powder
1 tsp salt
1/2 teaspoon cinnamon
2 large eggs
1/2 cup sugar
1/2 cup melted butter
1 teaspoon vanilla extract
3/4 cup apple sauce (or any extra large apple or 2 small ones, I just happen to have some applesauce already in the fridge to use up).
3 large or large apples or 4 smaller ones sliced or cubed

Oatmeal crumble
1/4 cup butter
1/2 cup oats
3 tbsp sugar (I like brown sugar, but white is fine)
1/4 tsp cinnamon (or more if you like it, I'd have 1 tsp for myself but Cormac isn't a cinnamon fan)

Directions

Preheat oven to 350F/180C

Grease a 9" or 10" round pan... I used a springform pan to make my life easier and lined it with baking paper. You could probably use a ~10" square pan.

Peel and slice your apples (if you really care, you can soak them in cold water with a few squirts of lemon juice to prevent browning but it really doesn't matter since you're just tossing them in the cake in the end).

Sift flour, baking powder, salt and cinnamon together.

Melt butter and leave it to cool.

In a another bowl or your mixer the eggs and sugar. Mix on high until its nearly syrupy and a bit pale colored. ~3 minutes.

Add the cool melted butter and the vanilla to the egg/sugar mix.

Add the applesauce and mix (if you have it).

Add the sliced apple pieces, mix gently until they are coated.

Add in the flour mix and mix until its well combined.

Start your crumble topping in a separate bowl. Use room temperature butter, and toss the oats, butter, sugar and cinnamon together. Squeeze it together until it forms pebbles of crumble topping.

Pour into your greased pan, sprinkle on the crumble topping, stick it in your oven for 50 minutes.